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Difficulty: HardRound Trips

A pilot flies a cargo plane from Airport A to Airport B at an average speed of 240240 mph. The pilot returns along the exact same route, but due to a strong headwind, the return flight averages only 160160 mph. If the total flying time for the entire round trip was exactly 55 hours, what is the one-way distance between Airport A and Airport B, in miles?

Answer: 480 miles

Answer

480
By setting up an algebraic equation representing the total time taken for both legs of the trip (using Time = Distance / Speed), we get d/240+d/160=5d/240 + d/160 = 5. Solving this equation by finding a common denominator of 480480 yields 5d/480=55d/480 = 5, which simplifies to d=480d = 480 miles.

Step-by-Step Solution

1
Define a variable for the unknown distance.
Let dd be the one-way distance in miles.
We need to find the one-way distance and relate it to the given times and speeds.
2
Express the time for each leg of the trip using the formula Time = Distance / Speed.
Outbound time = d240\frac{d}{240}, Return time = d160\frac{d}{160}.
The total time is given, so we need mathematical expressions for the time of each individual leg.
3
Set up an equation for the total time.
d240+d160=5\frac{d}{240} + \frac{d}{160} = 5
The sum of the outbound flight time and the return flight time equals the total round-trip flight time.
4
Find a common denominator to add the fractions.
The least common multiple of 240240 and 160160 is 480480. The equation becomes 2d480+3d480=5\frac{2d}{480} + \frac{3d}{480} = 5.
To solve for dd, we must combine the fractional terms into a single term.
5
Solve the equation for dd.
5d480=5⇒5d=2400⇒d=480\frac{5d}{480} = 5 \Rightarrow 5d = 2400 \Rightarrow d = 480.
Isolating dd gives the final one-way distance.

Key Concept

Solving round trip scenarios by setting up a total time equation: dv1+dv2=ttotal\frac{d}{v_1} + \frac{d}{v_2} = t_{total}
Estimated Time:2m 0s
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Topics

Round Trips

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