Word problems (extended practice)

{"questions":[{"content":"The first pipe fills the pool in $6$ hours, and the second pipe fills the pool in $4$ hours. How many hours will it take for both pipes to fill the pool, working simultaneously?[[fill_choice_big-3]][[image-35]]","widgets":{"fill_choice_big-3":{"type":"fill_choice_big","options":["$2.4$","$2.5$","$2.8$","$3$"],"placeholder":0,"answer":0},"image-35":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/09/bassei-n-01-2.svg","width":"400"}},"step":1,"hints":["Capacity of the first pipe: $\\frac{1}{6}$ pool per hour.","Capacity of the second pipe: $\\frac{1}{4}$ pool per hour.","Combined rate: $\\frac{1}{6} + \\frac{1}{4} = \\frac{2}{12} + \\frac{3}{12} = \\frac{5}{12}$.","Filling time: $\\frac{1}{\\frac{5}{12}} = \\frac{12}{5} = 2.4$ hours."]},{"content":"The boat traveled $48$ km along the river in $2$ hours and returned back in $3$ hours. Find the speed of the river flow.[[fill_choice_big-4]][[image-109]]","widgets":{"fill_choice_big-4":{"type":"fill_choice_big","options":["$4$","$5$","$6$","$8$"],"placeholder":0,"answer":0},"image-109":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/12/ship-1.svg","width":"400"}},"step":1,"hints":["Downstream speed: $48 : 2 = 24$ km/h.","Speed against the current: $48 : 3 = 16$ km/h.","Current speed: $\\frac{24 — 16}{2} = \\frac{8}{2} = 4$ km/h."]},{"content":"Two turners together produced $120$ parts in $4$ hours. The first turner makes $5$ parts per hour more than the second. How many parts does the second turner make per hour?[[fill_choice_big-5]][[image-190]]","widgets":{"fill_choice_big-5":{"type":"fill_choice_big","options":["$12.5$","$10$","$15$","$17.5$"],"placeholder":0,"answer":0},"image-190":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/obrazavr_konveer-01.svg","width":"400"}},"step":1,"hints":["Total productivity: $120 : 4 = 30$ parts per hour.","Let the second turner make $x$ parts per hour, then the first turner makes $x+5$.","$x + (x+5) = 30$.","$2x + 5 = 30$.","$2x = 25$.","$x = 12.5$ parts per hour."]},{"content":"A swimmer swam $60$ m against the flow of the river in $3$ minutes, and downstream in $2$ minutes. Find the speed of the river flow.[[fill_choice_big-6]][[image-278]]","widgets":{"fill_choice_big-6":{"type":"fill_choice_big","options":["$5$","$4$","$6$","$3$"],"placeholder":0,"answer":0},"image-278":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/10/swim.svg","width":"400"}},"step":1,"hints":["Speed upstream: $60 : 3 = 20$ m/min.","Downstream speed: $60 : 2 = 30$ m/min.","Flow speed: $\\frac{30 — 20}{2} = \\frac{10}{2} = 5$ m/min."]},{"content":"One mason can lay a wall in $12$ hours, and another in $8$ hours. How many hours will it take them to put the wall together?[[fill_choice_big-7]][[image-373]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$4.8$","$5$","$5.2$","$6$"],"placeholder":0,"answer":0},"image-373":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2026/03/stroitel-2.svg","width":"400"}},"step":1,"hints":["Work rate of the first: $\\frac{1}{12}$ walls per hour.","Work rate of the second: $\\frac{1}{8}$ walls per hour.","Combined rate: $\\frac{1}{12} + \\frac{1}{8} = \\frac{2}{24} + \\frac{3}{24} = \\frac{5}{24}$.","Working hours: $\\frac{1}{\\frac{5}{24}} = \\frac{24}{5} = 4.8$ hours."]},{"content":"A tourist sailed a boat $36$ km downstream of the river in $3$ hours, and against the current in $4$ hours. Find the speed of the river flow.[[fill_choice_big-8]][[image-475]]","widgets":{"fill_choice_big-8":{"type":"fill_choice_big","options":["$1.5$","$2$","$2.5$","$3$"],"placeholder":0,"answer":0},"image-475":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/lodka-1.svg","width":"400"}},"step":1,"hints":["Downstream speed: $36 : 3 = 12$ km/h.","Speed against the current: $36 : 4 = 9$ km/h.","Current speed: $\\frac{12 — 9}{2} = \\frac{3}{2} = 1.5$ km/h."]},{"content":"Two excavators dug a pit in $6$ hours. The first excavator can dig this pit in $10$ hours. How many hours will it take the second excavator to dig a pit?[[fill_choice_big-9]][[image-584]]","widgets":{"fill_choice_big-9":{"type":"fill_choice_big","options":["$15$","$12$","$18$","$20$"],"placeholder":0,"answer":0},"image-584":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/08/stroitel.svg","width":"400"}},"step":1,"hints":["Total productivity: $\\frac{1}{6}$ pit per hour.","Productivity of the first: $\\frac{1}{10}$ excavation per hour.","Work rate of the second: $\\frac{1}{6} — \\frac{1}{10} = \\frac{5}{30} — \\frac{3}{30} = \\frac{2}{30} = \\frac{1}{15}$.","Second working hours: $15$ hours."]},{"content":"The motor boat traveled $54$ km against the river in $3$ hours, and along the river in $2$ hours. Find the speed of the river flow.[[fill_choice_big-10]][[image-700]]","widgets":{"fill_choice_big-10":{"type":"fill_choice_big","options":["$4.5$","$5$","$5.5$","$6$"],"placeholder":0,"answer":0},"image-700":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/rychagi14_1.svg","width":"400"}},"step":1,"hints":["Speed against the current: $54 : 3 = 18$ km/h.","Downstream speed: $54 : 2 = 27$ km/h.","Current speed: $\\frac{27 — 18}{2} = \\frac{9}{2} = 4.5$ km/h."]},{"content":"One seamstress can sew a dress in $8$ hours, the second - in $12$ hours. How many hours will it take them to sew the dress together?[[fill_choice_big-11]][[image-840]]","widgets":{"fill_choice_big-11":{"type":"fill_choice_big","options":["$4.8$","$5$","$5.2$","$6$"],"placeholder":0,"answer":0},"image-840":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2026/02/1.svg","width":"400"}},"step":1,"hints":["First productivity: $\\frac{1}{8}$ dresses per hour.","Second productivity: $\\frac{1}{12}$ dresses per hour.","Combined rate: $\\frac{1}{8} + \\frac{1}{12} = \\frac{3}{24} + \\frac{2}{24} = \\frac{5}{24}$.","Working hours: $\\frac{1}{\\frac{5}{24}} = \\frac{24}{5} = 4.8$ hours."]},{"content":"The motor ship traveled $90$ km along the river in $3$ hours, and against the current in $5$ hours. Find the speed of the river flow.[[fill_choice_big-12]][[image-988]]","widgets":{"fill_choice_big-12":{"type":"fill_choice_big","options":["$6$","$7$","$8$","$9$"],"placeholder":0,"answer":0},"image-988":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/plavaniesudov2.svg","width":"400"}},"step":1,"hints":["Downstream speed: $90 : 3 = 30$ km/h.","Speed against the current: $90 : 5 = 18$ km/h.","Current speed: $\\frac{30 — 18}{2} = \\frac{12}{2} = 6$ km/h."]}]}

{"questions":[{"content":"The cyclist covered the distance between cities in $4$ hours, and the motorcyclist in $2.5$ hours. The speed of the motorcyclist is $18$ km/h greater than the speed of the cyclist. Find the speed of the cyclist.[[fill_choice_big-13]][[image-63]]","widgets":{"fill_choice_big-13":{"type":"fill_choice_big","options":["$30$","$25$","$35$","$28$"],"placeholder":0,"answer":0},"image-63":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/na-velike-velosiped-01-2-3.svg","width":"400"}},"step":1,"hints":["Let the speed of the cyclist be $x$ km/h, then the speed of the motorcyclist is $x+18$ km/h.","The distance is the same: $4x = 2.5(x+18)$.","$4x = 2.5x + 45$.","$1.5x = 45$.","$x = 30$ km/h."]},{"content":"Two pumps, working together, fill the tank in $5$ hours. The first pump fills the tank $6$ hours faster than the second. How many hours does it take the first pump to fill the tank?[[fill_choice_big-14]][[image-147]]","widgets":{"fill_choice_big-14":{"type":"fill_choice_big","options":["$8$","$10$","$12$","$15$"],"placeholder":0,"answer":0},"image-147":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/fireman-1.svg","width":"400"}},"step":1,"hints":["Let the first pump fill the tank in $x$ hours, then the second pump fills it in $x+6$ hours.","Work rate of the first: $\\frac{1}{x}$, of the second: $\\frac{1}{x+6}$.","$\\frac{1}{x} + \\frac{1}{x+6} = \\frac{1}{5}$.","$\\frac{2x+6}{x(x+6)} = \\frac{1}{5}$.","$5(2x+6) = x(x+6)$.","$10x + 30 = x^2 + 6x$.","$x^2 — 4x — 30 = 0$.","$x = \\frac{4 + \\sqrt{16 + 120}}{2} = \\frac{4 + \\sqrt{136}}{2} = \\frac{4 + 2\\sqrt{34}}{2} = 2 + \\sqrt{34} \\approx 8$ hours."]},{"content":"The plane flew at a speed of $600$ km/h, then increased the speed by $50$ km/h and flew all the way in $5$ hours. Find the distance if it is known that at the old speed he flew $1$ an hour longer.[[fill_choice_big-15]][[image-228]]","widgets":{"fill_choice_big-15":{"type":"fill_choice_big","options":["$3100$","$2500$","$3000$","$3250$"],"placeholder":0,"answer":0},"image-228":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/10/obrazavr_samolet.svg","width":"400"}},"step":1,"hints":["Let the plane fly at the old speed for $t$ hours, then at the new speed – $t-1$ hours.","$t + (t-1) = 5$.","$2t — 1 = 5$.","$t = 3$ hours with the old speed, $2$ hours with the new one.","Distance: $600 \\cdot 3 + 650 \\cdot 2 = 1800 + 1300 = 3100$ km."]},{"content":"The pedestrian walked from point A to point B at a speed of $5$ km/h, and back at a speed of $4$ km/h, spending $1$ an hour more on the return journey. Find the distance between the points.[[fill_choice_big-16]][[image-316]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$20$","$18$","$22$","$24$"],"placeholder":0,"answer":0},"image-316":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/12/obrazavr_perekrestok.svg","width":"400"}},"step":1,"hints":["Let the distance be $S$ km.","Time from A to B: $\\frac{S}{5}$, back: $\\frac{S}{4}$.","$\\frac{S}{4} — \\frac{S}{5} = 1$.","$\\frac{5S — 4S}{20} = 1$.","$\\frac{S}{20} = 1$.","$S = 20$ km."]},{"content":"Two tractor drivers plowed the field in $6$ hours. The first tractor driver could plow the field $5$ hours faster than the second. How many hours will it take the first tractor driver to plow the field?[[fill_choice_big-17]][[image-411]]","widgets":{"fill_choice_big-17":{"type":"fill_choice_big","options":["$10$","$8$","$12$","$15$"],"placeholder":0,"answer":0},"image-411":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/fermer-traktor-derevnya-1-1.svg","width":"400"}},"step":1,"hints":["Let the first tractor driver plow the field in $x$ hours, then the second one in $x+5$ hours.","$\\frac{1}{x} + \\frac{1}{x+5} = \\frac{1}{6}$.","$\\frac{2x+5}{x(x+5)} = \\frac{1}{6}$.","$6(2x+5) = x(x+5)$.","$12x + 30 = x^2 + 5x$.","$x^2 — 7x — 30 = 0$.","$x = \\frac{7 + \\sqrt{49 + 120}}{2} = \\frac{7 + 13}{2} = 10$ hours."]},{"content":"From two cities, the distance between which is $420$ km, a car and a bus simultaneously left towards each other. The speed of the car is $20$ km/h greater than the speed of the bus. Find the speed of the bus if they met after $3$ hours.[[fill_choice_big-18]][[image-513]]","widgets":{"fill_choice_big-18":{"type":"fill_choice_big","options":["$60$","$70$","$80$","$90$"],"placeholder":0,"answer":0},"image-513":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/avtobus-1.svg","width":"400"}},"step":1,"hints":["Let the speed of the bus be $x$ km/h, then the speed of the car is $x+20$ km/h.","Closing speed: $x + (x+20) = 2x + 20$.","Distance: $(2x+20) \\cdot 3 = 420$.","$6x + 60 = 420$.","$6x = 360$.","$x = 60$ km/h."]},{"content":"Two painters, working together, painted the fence in $4$ hours. The first painter would have painted this fence $2$ hours faster than the second. How many hours will it take the second painter to paint the fence?[[fill_choice_big-19]][[image-622]]","widgets":{"fill_choice_big-19":{"type":"fill_choice_big","options":["$9.1$","$8$","$10$","$12$"],"placeholder":0,"answer":0},"image-622":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/10/rialiti-shou-01.svg","width":"400"}},"step":1,"hints":["Let the second painter paint the fence in $x$ hours, then the first painter will paint it in $x-2$ hours.","$\\frac{1}{x-2} + \\frac{1}{x} = \\frac{1}{4}$.","$\\frac{2x-2}{x(x-2)} = \\frac{1}{4}$.","$4(2x-2) = x(x-2)$.","$8x — 8 = x^2 — 2x$.","$x^2 — 10x + 8 = 0$.","$x = \\frac{10 + \\sqrt{100 — 32}}{2} = \\frac{10 + \\sqrt{68}}{2} = \\frac{10 + 2\\sqrt{17}}{2} = 5 + \\sqrt{17} \\approx 9.1$ hours."]},{"content":"The truck traveled from point A to point B at a speed of $60$ km/h, and back at a speed of $40$ km/h. Find the average speed of the truck along the entire route.[[fill_choice_big-20]][[image-738]]","widgets":{"fill_choice_big-20":{"type":"fill_choice_big","options":["$48$","$50$","$52$","$45$"],"placeholder":0,"answer":0},"image-738":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/gruzoperevozki-dostavka-gazel-01-1.svg","width":"400"}},"step":1,"hints":["Let the distance between points be $S$ km.","Time there: $\\frac{S}{60}$, return time: $\\frac{S}{40}$.","Total time: $\\frac{S}{60} + \\frac{S}{40} = \\frac{2S + 3S}{120} = \\frac{5S}{120} = \\frac{S}{24}$.","Average speed: $\\frac{2S}{\\frac{S}{24}} = 48$ km/h."]},{"content":"$90$ parts were produced on three machines. The second machine produced $5$ more parts than the first, and the third one produced $10$ more parts than the second. How many parts did the first machine produce?[[fill_choice_big-21]][[image-861]]","widgets":{"fill_choice_big-21":{"type":"fill_choice_big","options":["$23.33$","$20$","$30$","$35$"],"placeholder":0,"answer":0},"image-861":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/04/zavod-1.svg","width":"400"}},"step":1,"hints":["Let the first machine produce $x$ parts.","Second: $x+5$, third: $(x+5)+10 = x+15$.","$x + (x+5) + (x+15) = 90$.","$3x + 20 = 90$.","$3x = 70$.","$x = 23.33$ details."]},{"content":"Two trains left simultaneously towards each other from two cities, the distance between which is $650$ km. The speed of the first train is $10$ km/h higher than the speed of the second. Find the speed of the second train if they met after $5$ hours.[[fill_choice_big-22]][[image-991]]","widgets":{"fill_choice_big-22":{"type":"fill_choice_big","options":["$60$","$65$","$70$","$75$"],"placeholder":0,"answer":0},"image-991":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/05/poezd-stancziya-.svg","width":"400"}},"step":1,"hints":["Let the speed of the second train be $x$ km/h, then the speed of the first is $x+10$ km/h.","Closing speed: $x + (x+10) = 2x + 10$.","Distance: $(2x+10) \\cdot 5 = 650$.","$10x + 50 = 650$.","$10x = 600$.","$x = 60$ km/h."]}]}

{"questions":[{"content":"A pedestrian left point A to point B at a speed of $4$ km/h. $2$ hours later, a cyclist followed him at a speed of $12$ km/h. How many hours after leaving will the cyclist catch up with the pedestrian?[[fill_choice_big-23]][[image-73]]","widgets":{"fill_choice_big-23":{"type":"fill_choice_big","options":["$1$","$1.5$","$2$","$2.5$"],"placeholder":0,"answer":0},"image-73":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/06/perehodit-dorogu-01.svg","width":"400"}},"step":1,"hints":["In $2$ hours the pedestrian walked: $4 \\cdot 2 = 8$ km.","Closing speed: $12 — 4 = 8$ km/h.","Time until meeting: $8 : 8 = 1$ hour."]},{"content":"Two operators typed the text in $6$ hours. The first operator could type this text in $10$ hours. How many hours will it take the second operator to type the text?[[fill_choice_big-24]][[image-147]]","widgets":{"fill_choice_big-24":{"type":"fill_choice_big","options":["$15$","$12$","$18$","$20$"],"placeholder":0,"answer":0},"image-147":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/12/pisatel-01.svg","width":"400"}},"step":1,"hints":["Overall productivity: $\\frac{1}{6}$ texts per hour.","First productivity: $\\frac{1}{10}$ text per hour.","Work rate of the second: $\\frac{1}{6} — \\frac{1}{10} = \\frac{5}{30} — \\frac{3}{30} = \\frac{2}{30} = \\frac{1}{15}$.","Second working hours: $15$ hours."]},{"content":"The tourist sailed a boat $24$ km downstream of the river and $16$ km against the current, spending $4$ hours for the entire journey. The speed of the river flow is $2$ km/h. Find the speed of the boat in still water.[[fill_choice_big-25]][[image-228]]","widgets":{"fill_choice_big-25":{"type":"fill_choice_big","options":["$10$","$8$","$12$","$9$"],"placeholder":0,"answer":0},"image-228":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/07/vodopad-obrazavr.svg","width":"400"}},"step":1,"hints":["Let the speed of the boat in still water be $x$ km/h.","Speed with the current: $x+2$, against the current: $x-2$.","Time: $\\frac{24}{x+2} + \\frac{16}{x-2} = 4$.","$\\frac{24(x-2) + 16(x+2)}{(x+2)(x-2)} = 4$.","$\\frac{24x — 48 + 16x + 32}{x^2-4} = 4$.","$\\frac{40x — 16}{x^2-4} = 4$.","$40x — 16 = 4x^2 — 16$.","$40x = 4x^2$.","$4x(x-10) = 0$.","$x = 10$ km/h."]},{"content":"Two teams of workers produced $240$ parts. The first team worked $4$ hours, the second - $6$ hours. How many parts did the second team produce per hour if together they produced $50$ parts per hour?[[fill_choice_big-26]][[image-316]]","widgets":{"fill_choice_big-26":{"type":"fill_choice_big","options":["$20$","$30$","$25$","$35$"],"placeholder":0,"answer":0},"image-316":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/Tipy-obshhestv_industrialnoe.svg","width":"400"}},"step":1,"hints":["Let the second team produce $x$ parts per hour, then the first team produces $50 — x$ parts per hour.","$4(50-x) + 6x = 240$.","$200 — 4x + 6x = 240$.","$200 + 2x = 240$.","$2x = 40$.","$x = 20$ parts per hour."]},{"content":"The bus traveled $180$ km in $3$ hours, and then another $120$ km in $2$ hours. Find the average speed of the bus along the entire route.[[fill_choice_big-27]][[image-495]]","widgets":{"fill_choice_big-27":{"type":"fill_choice_big","options":["$60$","$65$","$70$","$75$"],"placeholder":0,"answer":0},"image-495":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/11/obrazavr_school-bus.svg","width":"400"}},"step":1,"hints":["General route: $180 + 120 = 300$ km.","Total time: $3 + 2 = 5$ hours.","Average speed: $300 : 5 = 60$ km/h."]},{"content":"One pump can pump water out of a pool in $8$ hours, the other in $12$ hours. First, the first pump worked for $2$ hours, then the second one was connected to it. How long did it take to pump out the water?[[fill_choice_big-28]][[image-597]]","widgets":{"fill_choice_big-28":{"type":"fill_choice_big","options":["$5.6$","$5$","$7$","$8$"],"placeholder":0,"answer":0},"image-597":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/bassejn-plyvet-plovecz-plavaet-1-1.svg","width":"400"}},"step":1,"hints":["In $2$ hours the first pump pumped out: $\\frac{2}{8} = \\frac{1}{4}$ of the pool.","Remaining: $\\frac{3}{4}$ pool.","Combined rate: $\\frac{1}{8} + \\frac{1}{12} = \\frac{3}{24} + \\frac{2}{24} = \\frac{5}{24}$.","Collaboration time: $\\frac{3}{4} : \\frac{5}{24} = \\frac{3}{4} \\cdot \\frac{24}{5} = \\frac{18}{5} = 3.6$ hours.","Total time: $2 + 3.6 = 5.6$ hours."]},{"content":"The boat traveled $36$ km along the river in $2$ hours, and against the current - $36$ km in $3$ hours. Find the speed of the river flow.[[fill_choice_big-29]][[image-721]]","widgets":{"fill_choice_big-29":{"type":"fill_choice_big","options":["$3$","$4$","$2$","$5$"],"placeholder":0,"answer":0},"image-721":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/12/ship-1.svg","width":"400"}},"step":1,"hints":["Downstream speed: $36 : 2 = 18$ km/h.","Speed against the current: $36 : 3 = 12$ km/h.","Current speed: $\\frac{18 — 12}{2} = \\frac{6}{2} = 3$ km/h."]},{"content":"Two cars left simultaneously from one point in the same direction. The speed of the first car is $80$ km/h, the second is $60$ km/h. After how many hours the distance between them will be $100$ km?[[fill_choice_big-30]][[image-837]]","widgets":{"fill_choice_big-30":{"type":"fill_choice_big","options":["$5$","$4$","$6$","$8$"],"placeholder":0,"answer":0},"image-837":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/mashina.svg","width":"400"}},"step":1,"hints":["Removal speed: $80 — 60 = 20$ km/h.","Time: $100 : 20 = 5$ hours."]},{"content":"There were $800$ liters of water in the tank. Water flows out through the first hose at a speed of $20$ l/min, and through the second - $30$ l/min. First, we opened the first hose for $10$ minutes, then opened the second. How many minutes after opening the second hose will the tank be empty?[[fill_choice_big-31]][[image-960]]","widgets":{"fill_choice_big-31":{"type":"fill_choice_big","options":["$12$","$10$","$15$","$18$"],"placeholder":0,"answer":0},"image-960":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/02/pozharnyj-tushit-ogon.svg","width":"400"}},"step":1,"hints":["In $10$ minutes the following flowed out: $20 \\cdot 10 = 200$ l.","Remaining: $800 — 200 = 600$ l.","Total speed: $20 + 30 = 50$ l/min.","Time: $600 : 50 = 12$ minutes."]},{"content":"Two runners started at the same time in the same direction. The speed of the first runner is $12$ km/h, the second - $8$ km/h. After how many minutes will the distance between them become $1$ km?[[fill_choice_big-32]][[image-1318]]","widgets":{"fill_choice_big-32":{"type":"fill_choice_big","options":["$15$","$10$","$20$","$25$"],"placeholder":0,"answer":0},"image-1318":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/10/run.svg","width":"400"}},"step":1,"hints":["Removal speed: $12 — 8 = 4$ km/h.","Time: $1 : 4 = 0.25$ hours = $15$ minutes."]}]}

{"questions":[{"content":"A motorcyclist left point A to point B at a speed of $40$ km/h. After $1$ hour, a car left point B to point A at a speed of $60$ km/h. Distance between points $160$ km. How many hours after the motorcyclist leaves will they meet?[[fill_choice_big-33]][[image-68]]","widgets":{"fill_choice_big-33":{"type":"fill_choice_big","options":["$2.2$","$2$","$2.5$","$3$"],"placeholder":0,"answer":0},"image-68":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/11/italiya-3.svg","width":"400"}},"step":1,"hints":["In $1$ hour the motorcyclist traveled: $40 \\cdot 1 = 40$ km.","Distance remaining: $160 — 40 = 120$ km.","Closing speed: $40 + 60 = 100$ km/h.","Time until the meeting after leaving the car: $120 : 100 = 1.2$ hours.","Total time: $1 + 1.2 = 2.2$ hours."]},{"content":"Two workers, working together, completed the order in $4$ hours. The first worker could complete this order in $6$ hours. How many hours will it take the second worker to complete the order?[[fill_choice_big-34]][[image-112]]","widgets":{"fill_choice_big-34":{"type":"fill_choice_big","options":["$12$","$10$","$15$","$8$"],"placeholder":0,"answer":0},"image-112":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/06/Tipy-obshhestv_industrialnoe.svg","width":"400"}},"step":1,"hints":["Total productivity: $\\frac{1}{4}$ orders per hour.","First productivity: $\\frac{1}{6}$ orders per hour.","Work rate of the second: $\\frac{1}{4} — \\frac{1}{6} = \\frac{3}{12} — \\frac{2}{12} = \\frac{1}{12}$.","Second working hours: $12$ hours."]},{"content":"The passenger train covered $300$ km in $5$ hours, and the freight train covered $240$ km in $6$ hours. How much is the speed of a passenger train greater than the speed of a freight train?[[fill_choice_big-35]][[image-164]]","widgets":{"fill_choice_big-35":{"type":"fill_choice_big","options":["$20$","$15$","$25$","$30$"],"placeholder":0,"answer":0},"image-164":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2023/03/poezd-elektrichka-1.svg","width":"400"}},"step":1,"hints":["Passenger speed: $300 : 5 = 60$ km/h.","Freight speed: $240 : 6 = 40$ km/h.","Speed difference: $60 — 40 = 20$ km/h."]},{"content":"Two pipes are installed into the pool. Through the first pipe the pool is filled in $10$ hours, through the second - in $15$ hours. First, they opened the first pipe at $3$ hours, then they opened the second. How long did it take to fill the pool?[[fill_choice_big-36]][[image-224]]","widgets":{"fill_choice_big-36":{"type":"fill_choice_big","options":["$7.2$","$8$","$7.8$","$9$"],"placeholder":0,"answer":0},"image-224":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/07/bassei-n-01-2.svg","width":"400"}},"step":1,"hints":["In $3$ hours the first pipe filled: $\\frac{3}{10}$ pool.","Remaining: $\\frac{7}{10}$ pool.","Combined rate: $\\frac{1}{10} + \\frac{1}{15} = \\frac{3}{30} + \\frac{2}{30} = \\frac{5}{30} = \\frac{1}{6}$.","Collaboration time: $\\frac{7}{10} : \\frac{1}{6} = \\frac{7}{10} \\cdot 6 = \\frac{42}{10} = 4.2$ hours.","Total time: $3 + 4.2 = 7.2$ hours."]},{"content":"Distance between piers $48$ km. The boat covered this distance along the current in $2$ hours, and against the current in $3$ hours. Find the speed of the river flow.[[fill_choice_big-37]][[image-284]]","widgets":{"fill_choice_big-37":{"type":"fill_choice_big","options":["$4$","$3$","$5$","$6$"],"placeholder":0,"answer":0},"image-284":{"type":"image","url":"/wp-content/themes/Main/img/math-port/2022/12/ship-1.svg","width":"400"}},"step":1,"hints":["Downstream speed: $48 : 2 = 24$ km/h.","Speed against the current: $48 : 3 = 16$ km/h.","Current speed: $\\frac{24 — 16}{2} = \\frac{8}{2} = 4$ km/h."]}]}