A vehicle journeyed from City X to City Y without any breaks, covering a total distance of 3n miles, where n > 0. The vehicle maintained an average speed of w miles per hour for the first n miles, and for the entire 3n miles, it averaged a speed of 4w/3 miles per hour. What was the average speed of the vehicle, in miles per hour, during the last 2n miles?

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8w/5

Correct

16w/3

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Official Explanation

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The total distance is 3n. The average speed for the first n miles is w, and for the entire 3n miles, it is 4w/3. We can set up the equation for average speed: n/w + 2n/x = 3n/(4w/3). This simplifies to n/w…

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Comments

MohamedApr 16, 2025

Any shortcuts for solving this faster?

OlgaMar 31, 2025

Thank you very much!

What this question tests

What it tests

Your application of distance = rate × time to trains, boats, and commuters, including relative speed.

Common trap

Mixing units (miles per hour vs. minutes) or averaging speeds — average speed is total distance over total time.