An express delivery drone flies from Station Alpha to Station Beta at a constant speed of … — GMAT

An express delivery drone flies from Station Alpha to Station Beta at a constant speed of $60$ miles per hour against a headwind. On the return flight along the exact same path from Station Beta to Station Alpha, with the wind acting as a tailwind of identical strength, the drone travels at a constant speed of $90$ miles per hour. If the entire round-trip flight took a total of $5$ hours, what is the distance, in miles, between Station Alpha and Station Beta?

Answer: 180 miles

Answer

The distance between Station Alpha and Station Beta is 180 miles.

To find the distance

D

, set up the total time equation:

\frac{D}{60} + \frac{D}{90} = 5

. Finding the common denominator yields

\frac{5D}{180} = 5

, leading directly to

D = 180

miles.

Step-by-Step Solution

Define the unknown variable and write time expressions for each leg.

Let

D

be the distance between Station Alpha and Station Beta. Outbound time is

\frac{D}{60}

hours and return time is

\frac{D}{90}

hours.

Using the rate-time-distance formula

t = \frac{d}{r}

allows expressing unknown time components using distance.

Set up an equation for total round-trip time.

\frac{D}{60} + \frac{D}{90} = 5

The sum of the time spent on the outbound leg and the return leg equals the total given flight time of

5

hours.

Solve the algebraic equation for

D

Finding a common denominator of

180

gives

\frac{3D + 2D}{180} = 5 \implies \frac{5D}{180} = 5 \implies 5D = 900 \implies D = 180

Multiplying both sides by

180

clears denominators and isolates

D

Key Concept

Rate, Time, and Distance Relationship

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