A passenger train and a cargo train both travel along parallel tracks on a 120-mile route … — GMAT

A passenger train and a cargo train both travel along parallel tracks on a $120$ -mile route between Station P and Station Q. The passenger train travels at a constant speed of $50$ miles per hour for the entire trip. The cargo train completes the first $60\%$ of the total distance at a constant speed of $30$ miles per hour and the remaining $40\%$ of the distance at a constant speed of $60$ miles per hour. By what percentage is the average speed of the passenger train for the entire trip greater than the average speed of the cargo train for the entire trip?

A
$11\frac{1}{9}\%$
B
$20\%$
C
$25\%$
$33\frac{1}{3}\%$ Answer
E
$40\%$

Answer

The average speed of the passenger train is

33\frac{1}{3}\%

greater than the average speed of the cargo train.

The correct answer accurately determines the total travel time of the cargo train (

3.2

hours) to find its true average speed (

37.5

mph). Comparing the passenger train's speed (

50

mph) against this baseline gives

\frac{50 - 37.5}{37.5} = \frac{1}{3}

, which corresponds to

33\frac{1}{3}\%

Step-by-Step Solution

Calculate the travel time and average speed of the passenger train.

The passenger train travels

120

miles at

50

mph, so its average speed is

50

mph.

The passenger train maintains a single constant speed throughout the trip.

Calculate the distance and travel time for each leg of the cargo train's trip.

Leg 1 distance:

60\%

120 = 72

miles; Leg 1 time:

\frac{72}{30} = 2.4

hours. Leg 2 distance:

40\%

120 = 48

miles; Leg 2 time:

\frac{48}{60} = 0.8

hours.

Time equals distance divided by speed for each specific segment.

Determine the total travel time and overall average speed of the cargo train.

Total time =

2.4 + 0.8 = 3.2

hours. Cargo train average speed =

\frac{120\text{ miles}}{3.2\text{ hours}} = 37.5

mph.

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

Calculate by what percentage the passenger train's average speed is greater than the cargo train's average speed.

Percentage increase =

\frac{50 - 37.5}{37.5} \times 100\% = \frac{12.5}{37.5} \times 100\% = \frac{1}{3} \times 100\% = 33\frac{1}{3}\%

The baseline for 'percent greater than the cargo train' is the cargo train's speed (

37.5

mph).

Key Concept

Average Speed for Multi-Leg Journeys and Percentage Difference Baseline

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