A motorist travels from Town A to Town B, a distance of 120 miles, at a constant speed of … — GMAT

A motorist travels from Town A to Town B, a distance of $120$ miles, at a constant speed of $60$ miles per hour. On the return trip from Town B to Town A along the exact same route, heavy traffic slows the vehicle's speed to $20$ miles per hour for the first half of the distance. At what constant speed, in miles per hour, must the motorist travel for the remaining half of the return trip so that the average speed for the entire $240$ -mile round trip is $32$ miles per hour?

A
16
24Answer
C
28
D
36
E
44

Answer

24 miles per hour

The correct answer is 24 miles per hour. To achieve an overall average speed of 32 mph over the total 240-mile trip, the entire journey must take exactly 7.5 hours (

240 / 32 = 7.5

). The outbound 120-mile trip at 60 mph takes 2 hours (

120 / 60 = 2

). The first 60 miles of the return trip at 20 mph takes 3 hours (

60 / 20 = 3

). This leaves

7.5 - 5 = 2.5

hours to complete the final 60 miles. Dividing 60 miles by 2.5 hours yields a required speed of 24 mph.

Step-by-Step Solution

Calculate the total time required for the entire round trip.

\text{Total Time} = \frac{\text{Total Distance}}{\text{Average Speed}} = \frac{240\text{ miles}}{32\text{ mph}} = 7.5\text{ hours}

Average speed is defined as total distance divided by total time.

Calculate the time taken for the outbound trip and the first half of the return trip.

\text{Outbound Time} = \frac{120}{60} = 2\text{ hours}; \quad \text{Return Leg 1 Time} = \frac{60}{20} = 3\text{ hours}

Time equals distance divided by rate for each specific segment.

Determine the remaining time and required speed for the final segment of

60

miles.

\text{Remaining Time} = 7.5 - (2 + 3) = 2.5\text{ hours}; \quad \text{Required Speed} = \frac{60\text{ miles}}{2.5\text{ hours}} = 24\text{ mph}

Dividing the remaining

60

miles by the remaining

2.5

hours gives the required speed.

Key Concept

Average speed for multi-leg journeys must always be calculated as Total Distance divided by Total Time, not by taking the arithmetic mean of individual speeds.

Estimated Time:2m 0s

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