FREE GMA Word Problems (Rate, Time, Distance) Questions and Answers

Question 1

Two trains start at the same time from two stations 300 km apart and travel towards each other. One train travels at 60 km/h and the other at 90 km/h. How long will it take for them to meet?

Accepted Answer

2 hours

Answer

Since the trains are moving towards each other, their speeds are added to find their relative speed. The combined speed is 60 km/h + 90 km/h = 150 km/h. To find the time it takes for them to meet, divide the total distance by their combined speed (Time = Distance / Speed).

Question 2

A car travels to a destination at 40 km/h and returns on the same route at 60 km/h. What is the average speed for the entire trip?

Accepted Answer

48 km/h

Answer

Average speed is the total distance divided by the total time. It is not the simple average of the speeds because more time is spent traveling at the slower speed. The formula for two equal distances at different speeds is (2 * Speed1 * Speed2) / (Speed1 + Speed2), which is (2 * 40 * 60) / (40 + 60) = 48 km/h.

Question 3

A cyclist starts from point A at 10:00 AM, traveling at 15 km/h. A motorcyclist starts from the same point at 12:00 PM, traveling at 25 km/h in the same direction. At what time will the motorcyclist catch up with the cyclist?

Accepted Answer

3:00 PM

Answer

The cyclist has a 2-hour head start, covering a distance of 15 km/h * 2 h = 30 km. The motorcyclist gains on the cyclist at a relative speed of 25 km/h - 15 km/h = 10 km/h. The time to catch up is the head start distance divided by the relative speed (30 km / 10 km/h = 3 hours), which is 3 hours after the motorcyclist starts at 12:00 PM.

Question 4

A bus travels a distance of 450 km. If it travels at a speed of 60 km/h, how much extra time will it take if it stops for 10 minutes every hour?

Accepted Answer

70 minutes

Answer

The travel time without stops is 450 km / 60 km/h = 7.5 hours. The bus will stop at the end of the 1st, 2nd, 3rd, 4th, 5th, 6th, and 7th hour. It will not make a stop at the end of the journey, so there are 7 stops in total. The total stoppage time is 7 stops * 10 minutes/stop = 70 minutes.

Question 5

A boat's speed in still water is 13 km/h and the speed of the stream is 4 km/h. Find the time taken by the boat to go 68 km downstream.

Accepted Answer

4 hours

Answer

When traveling downstream, the speed of the stream adds to the boat's speed. The effective downstream speed is 13 km/h + 4 km/h = 17 km/h. Time is calculated as Distance / Speed, so the time taken is 68 km / 17 km/h = 4 hours.

(GMA) General Mental Ability Practice Test

(GMA) General Mental Ability Practice Test

FREE GMA Word Problems (Rate, Time, Distance) Questions and Answers