# Word Problems - Proportions, Speed & Time: Problems with Solutions

Problem 1 sent by Ksenia
The sum of three consecutive even numbers is 78. What are the numbers?
Problem 2
Kayla climbs 60 steps in 40 seconds. At that rate, how many steps could she climb in 150 seconds?
Problem 3
From January through June, 46200 immigrants applied for citizenship. During this same period last year, 120000 immigrants applied. What is the percentage of decrease?
A store sold cherries in the afternoon twice as many as in the morning. Throughout the day were sold 360 kg. How many kilograms were sold in the afternoon?
Problem 5
Two cyclists leave at the same time from the same place on a circle. The first does a lap in 3 minutes and the other in 4 minutes. After how much time will they meet again at the starting point?
Problem 6 sent by Zaki
We give the following information about a race hedge.
There are 10 hurdles. The distance between consecutive two lines (that is to say which follow) is 9.14 m. There are 13.72 m between the starting line and the first line and the last hurdle between 14.02 m and line arrival. Each hurdle measures 106 cm in height.

What is the length(in centimeters) of the track?
Problem 7
If you divide a number into 3 equal groups and then divide each group in half, you end up with 13. What number did you start with?
Problem 8
A car runs 375 km in 3 hours. What's the car's speed?
Problem 9
A train leaves from city A at 9:15 and arrives at city B at 10:35. If the speed of the train is 180 km/h, what's the distance between the two cities?
Problem 10
Tim rides his bike to school and arrives in 15 minutes. If his speed is 8 m/s, what's the distance between the school and his home?

Problem 11
A cyclist climbs a hill with a length of 400 m with a speed of 7.2 km/h. When descending, the speed is two times greater. How much time is necessary for the cyclist to climb and descend the hill?
Problem 12
The distance between 2 subway stations is 4.5 km. If the train leaves at 9:10 from one station and its speed is 90 km/h, what time does it get to the next station?
Problem 13
A car runs the distance between cities A and B in 3 hours and 30 minutes with a speed of 180 km/h. A motorcyclist runs the same distance in 5 hours. What's the speed of the motorcycle?
Problem 14
The distance between 2 cities is 1200 km. A car runs a quarter of the way with a speed of 80 km/h and the rest with a speed of 120 km/h. How much time is necessary to run the whole distance?
Problem 15
Joe and John are planning to paint a house together. John thinks that if he worked alone, it would take him 3 times more than if he worked with Joe to paint the whole house. Working together, they complete the job in $24$ hours. How long would it take each of them, working alone, to finish the job?

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