An express delivery truck travels from Warehouse A to Warehouse B along a 180-mile route. … — GMAT

An express delivery truck travels from Warehouse A to Warehouse B along a $180$ -mile route. For the first $60$ miles, the truck maintains a constant speed of $v$ miles per hour. For the remaining $120$ miles, heavy traffic reduces its constant speed to $\frac{v}{2}$ miles per hour. If the average speed of the truck for the entire $180$ -mile trip was $36$ miles per hour, what was the truck's speed $v$ , in miles per hour, during the first $60$ miles?

A
$36$
B
$48$
C
$54$
$60$ Answer
E
$75$

Answer

The speed

v

during the first leg of the trip was

60

miles per hour.

The correct answer is

60

miles per hour. Total trip time is the sum of time on the first leg (

\frac{60}{v}

hours) and time on the second leg (

\frac{120}{v/2} = \frac{240}{v}

hours), giving a total time of

\frac{300}{v}

hours. Since average speed equals total distance divided by total time,

\frac{180}{300/v} = \frac{3v}{5} = 36

, solving to

v = 60

Step-by-Step Solution

Express the time spent on each leg of the trip in terms of

v

Leg 1 time:

t_1 = \frac{60}{v}

hours. Leg 2 time:

t_2 = \frac{120}{v/2} = \frac{240}{v}

hours.

Time equals distance divided by rate. The rate for the second leg is half of

v

Calculate the total time for the entire

180

-mile trip in terms of

v

Total time

T = t_1 + t_2 = \frac{60}{v} + \frac{240}{v} = \frac{300}{v}

hours.

Summing the travel times of both legs gives the total trip duration.

Set up the average speed equation using total distance divided by total time.

\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{180}{\frac{300}{v}} = \frac{180v}{300} = \frac{3v}{5}$.

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

Equate the average speed expression to the given value of

36

mph and solve for

v

\frac{3v}{5} = 36 \implies 3v = 180 \implies v = 60$ miles per hour.

Multiplying both sides by

5

and dividing by

3

isolates

v

Key Concept

Average speed for a multi-leg journey is always calculated as total distance divided by total time, not by taking the arithmetic mean of the speeds.

Estimated Time:2m 0s

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