A ferry travels from Port Alpha to Port Beta across a bay, a distance of 30 miles, at a co… — GMAT

A ferry travels from Port Alpha to Port Beta across a bay, a distance of $30$ miles, at a constant speed of $15$ miles per hour. On the return trip from Port Beta to Port Alpha along the exact same route, the ferry travels at a constant speed of $30$ miles per hour. What is the ferry's average speed, in miles per hour, for the entire round trip?

Answer: 20 miles per hour

Answer

The ferry's average speed for the entire round trip is

20

miles per hour.

Average speed is found by dividing the total distance traveled by the total time taken. The round trip consists of two 30-mile legs, making the total distance 60 miles. The outbound leg takes 2 hours (30 / 15), while the return leg takes 1 hour (30 / 30), giving a total time of 3 hours. Dividing 60 miles by 3 hours yields an average speed of 20 miles per hour.

Step-by-Step Solution

Calculate outbound trip duration

2 hours

Dividing distance by rate gives time:

30 / 15 = 2

hours.

Calculate return trip duration

1 hour

Dividing distance by rate gives time:

30 / 30 = 1

hour.

Calculate total distance and total time

60 miles in 3 hours

Total distance is

30 + 30 = 60

miles, and total time is

2 + 1 = 3

hours.

Calculate overall average speed

20 mph

Average speed is total distance divided by total time:

60 / 3 = 20

mph.

Key Concept

Average speed for any multi-leg or round-trip journey is defined as Total Distance divided by Total Time, rather than the simple arithmetic mean of the speeds.

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