Speedy travel

Algebra Level 2

Achilles decides to jog between point A and point B. He covers the distance at a rate of 10 miles per hour.

After a pleasant chat with Zeno and the Tortoise, Achilles speeds his pace up. He runs from point B back to point A along the identical route he took to get to point B, except that this time he covers the distance at a rate of 15 miles per hour.

If you combine the two journeys, what was his average rate of speed, to two decimal places, in miles per hour?

The answer is 12.00.

2 solutions

Denton Young
May 11, 2017

Let us say, for purposes of calculation, that the distance between points A and B along the specified route is 60 miles. Since it wasn't given, we can use any number we want.

Then: Total journey = 60 * 2 = 120 miles

Total time: (There) 60/10 = 6 hours, (back) 60/15 = 4 hours, 6 + 4 = 10 hours total

Average combined speed: 120/10 = 12.00 mph

Richard Costen
May 11, 2017

Or a more general solution. Let $d$ be the distance travelled in one direction. Then $2d$ is the total distance travelled. The time taken to travel in one direction is $\frac{d}{10}$ and the time to travel back is $\frac{d}{15}$ . The total time is $\frac{d}{10}+\frac{d}{15}$ . The average speed is distance/time or $\frac{2d}{\frac{d}{10}+\frac{d}{15}}$ . After simplifying the fraction, the $d$ 's cancel out and the answer is $\boxed{12}$ .

Speedy travel

The answer is 12.00.

2 solutions

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