A commuter drives a total distance of 60 miles from home to work. Due to heavy morning tra… — GMAT

A commuter drives a total distance of $60$ miles from home to work. Due to heavy morning traffic, the commuter travels the first $30$ miles at a constant speed of $30$ miles per hour. At what constant speed, in miles per hour, must the commuter travel the remaining $30$ miles to achieve an average speed of $40$ miles per hour for the entire $60$ -mile trip?

A
$45$
B
$48$
C
$50$
$60$ Answer
E
$75$

Answer

The commuter must travel the remaining

30

miles at a speed of

60

miles per hour.

The total trip distance is

60

miles and the desired overall average speed is

40

miles per hour, requiring a total time of

1.5

hours. Since traveling the first

30

miles at

30

miles per hour takes

1

hour, only

0.5

hours remain to complete the remaining

30

miles. Traveling

30

miles in

0.5

hours requires an average speed of

60

miles per hour.

Step-by-Step Solution

Calculate the total time required for the entire trip using

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

\text{Total Time} = \frac{60 \text{ miles}}{40 \text{ mph}} = 1.5 \text{ hours}

Average speed for a multi-leg trip is defined strictly as total distance divided by total time.

Calculate the time spent on the first leg of the trip.

\text{Time for Leg 1} = \frac{30 \text{ miles}}{30 \text{ mph}} = 1.0 \text{ hour}

Using

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

for the first

30

miles.

Determine the remaining time available for the second leg of the trip.

\text{Time for Leg 2} = 1.5 \text{ hours} - 1.0 \text{ hour} = 0.5 \text{ hours}

The sum of the times for both legs must equal the total required trip time.

Calculate the required constant speed for the remaining

30

miles.

\text{Speed for Leg 2} = \frac{30 \text{ miles}}{0.5 \text{ hours}} = 60 \text{ mph}

Dividing the remaining distance by the remaining time gives the required speed for the second leg.

Key Concept

Average Speed Formula (

V_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}}

)

Estimated Time:2m 0s

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Answer

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