A commuter travels to work along a straight route at a constant speed of 40 miles per hour… — GMAT

A commuter travels to work along a straight route at a constant speed of $40$ miles per hour. On the return trip along the exact same route, traffic delays reduce the average speed to $24$ miles per hour. If the return trip takes $40$ minutes longer than the trip to work, what is the total distance, in miles, traveled by the commuter for the round trip?

Answer: 80 miles

Answer

The total distance traveled by the commuter for the round trip is 80 miles.

The total distance for the round trip is 80 miles. By expressing time as distance divided by speed, the outbound trip takes

\frac{D}{40}

hours and the return trip takes

\frac{D}{24}

hours. Since the return trip takes

40

minutes (

\frac{2}{3}

hours) longer, setting up the equation

\frac{D}{24} - \frac{D}{40} = \frac{2}{3}

yields

D = 40

miles for one way. The round-trip distance is

2 \times 40 = 80

miles.

Step-by-Step Solution

Define variables for the one-way distance and expressions for the travel time of each leg.

Let

D

represent the one-way distance in miles. Outbound time

t_1 = \frac{D}{40}

hours; return time

t_2 = \frac{D}{24}

hours.

Using the relation

\text{Time} = \frac{\text{Distance}}{\text{Speed}}

expresses time in terms of a single unknown variable.

Convert the given time difference from minutes to hours.

40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}

Speeds are given in miles per hour, so time units must be in hours for dimensional consistency.

Formulate the equation representing the time difference and solve for

D

\frac{D}{24} - \frac{D}{40} = \frac{2}{3} \implies \frac{2D}{120} = \frac{2}{3} \implies \frac{D}{60} = \frac{2}{3} \implies D = 40 \text{ miles}

Subtracting the faster outbound time from the slower return time equals the time difference.

Compute the total distance for the entire round trip.

\text{Total distance} = 2 \times D = 2 \times 40 = 80 \text{ miles}

The question asks for the round-trip distance, which includes both the outbound and return journeys (

2D

Key Concept

Rate, Time, and Distance Problems

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