Free GMA Word Problems (Rate, Time, Distance) Questions and Answers 1 — 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?
- 1.5 hours
- 2 hours (Correct answer)
- 2.5 hours
- 3 hours
Correct answer: 2 hours
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?
- 50 km/h
- 52 km/h
- 48 km/h (Correct answer)
- 45 km/h
Correct answer: 48 km/h
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?
- 2:30 PM
- 4:00 PM
- 3:30 PM
- 3:00 PM (Correct answer)
Correct answer: 3:00 PM
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?
- 60 minutes
- 70 minutes (Correct answer)
- 75 minutes
- 80 minutes
Correct answer: 70 minutes
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.
- 3 hours
- 5 hours
- 4 hours (Correct answer)
- 4.5 hours
Correct answer: 4 hours
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.
Question 6: A person crosses a 600-meter long street in 5 minutes. What is his speed in km per hour?
- 3.6 km/h
- 7.2 km/h (Correct answer)
- 8.4 km/h
- 10 km/h
Correct answer: 7.2 km/h
First, convert the units. The distance is 600 m = 0.6 km, and the time is 5 minutes = 5/60 hours. Speed is calculated as Distance / Time, so Speed = 0.6 km / (5/60 h) = 0.6 * (60/5) = 0.6 * 12 = 7.2 km/h.
Free GMA Word Problems (Rate, Time, Distance) Questions and Answers 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?