GMA Word Problems (Rate, Time, Distance) 2 — Questions and Answers

Question 1: A car travels at 60 km/h. How long does it take to travel 180 km?

2 hours
3 hours (Correct answer)
4 hours
2.5 hours

Correct answer: 3 hours

Time = Distance ÷ Speed = 180 ÷ 60 = 3 hours.

The fundamental rate-time-distance formula is: Distance = Speed × Time, rearranged as Time = Distance ÷ Speed. Plugging in: Time = 180 km ÷ 60 km/h = 3 hours. Always confirm the units are consistent (km and km/h give hours as the result).

Question 2: Two trains start from opposite ends of a 300 km track and travel toward each other. Train A travels at 80 km/h and Train B at 70 km/h. How long before they meet?

1.5 hours
2 hours (Correct answer)
2.5 hours
3 hours

Correct answer: 2 hours

Combined speed = 80+70=150 km/h. Time = 300÷150 = 2 hours.

When two objects move toward each other, their speeds add together. The combined closing speed is 80+70=150 km/h. The total distance to close is 300 km. Time = 300÷150 = 2 hours. This is a classic 'meeting point' problem where the key insight is combining velocities.

Question 3: A worker can complete a job in 6 hours. A second worker can complete the same job in 3 hours. Working together, how long will it take?

4.5 hours
4 hours
3 hours
2 hours (Correct answer)

Correct answer: 2 hours

Worker 1 rate: 1/6 job/hr. Worker 2 rate: 1/3 job/hr. Combined: 1/6+1/3=1/6+2/6=3/6=1/2 job/hr. Time = 1÷(1/2)=2 hours.

Combined work problems use rates (fraction of job completed per unit time). Worker 1 completes 1/6 of the job per hour; Worker 2 completes 1/3 per hour. Together they complete 1/6+2/6=3/6=1/2 job per hour. Time to complete one whole job = 1÷(1/2)=2 hours.

Question 4: A cyclist rides at 20 km/h for 2 hours and then at 15 km/h for 1 hour. What is the total distance covered?

45 km
55 km (Correct answer)
60 km
70 km

Correct answer: 55 km

First segment: 20×2=40 km. Second segment: 15×1=15 km. Total: 40+15=55 km.

For multi-segment journeys, calculate each segment independently. Segment 1: 20 km/h × 2 h = 40 km. Segment 2: 15 km/h × 1 h = 15 km. Total distance = 40+15 = 55 km. The key is that distance = speed × time applies to each segment separately before summing.

Question 5: A train covers a distance of 240 km in 4 hours. What is its average speed?

40 km/h
50 km/h
60 km/h (Correct answer)
70 km/h

Correct answer: 60 km/h

Speed = Distance ÷ Time = 240 ÷ 4 = 60 km/h.

Average speed for a journey is total distance divided by total time. Speed = 240 km ÷ 4 h = 60 km/h. 'Average speed' is used because even if the train had varying speeds throughout, the only information given (total distance and total time) yields the average.

Question 6: A boat travels upstream at 8 km/h and downstream at 12 km/h. What is the speed of the current?

2 km/h (Correct answer)
4 km/h
10 km/h
20 km/h

Correct answer: 2 km/h

Speed of current = (Downstream speed - Upstream speed) ÷ 2 = (12-8)÷2 = 4÷2 = 2 km/h.

Let boat speed in still water = b, current speed = c. Downstream: b+c=12; Upstream: b-c=8. Subtracting: 2c=4, so c=2 km/h. The boat's still-water speed is b=10 km/h. Alternatively: current = (downstream - upstream) ÷ 2 = (12-8)÷2 = 2 km/h.

GMA Word Problems (Rate, Time, Distance) 2

A car travels at 60 km/h.
How long does it take to travel 180 km?