Question

John can jog twice as fast as he can walk. He was able to jog first 5miles to his grandmother’s house, but then he got tired and walked the remaining 2miles. If the total trip took 0.9 hours, then what was his average jogging speed?

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Let the walking speed be x miles per hour. Then, the jogging speed is 2x miles per hour.

Given that John jogged 5 miles and walked 2 miles, and that the total trip took 0.9 hours, we can set up the following equations for the time spent jogging and walking:

\text{jogging time} = \frac{5}{2x}

\text{walking time} = \frac{2}{x}

The total time is the sum of these two times:

\frac{5}{2x} + \frac{2}{x} = 0.9

To solve forx , we find a common denominator and combine the fractions:

\frac{5}{2x} + \frac{2}{x} = \frac{5}{2x} + \frac{4}{2x} = \frac{9}{2x}

So,

\frac{9}{2x} = 0.9

Multiply both sides by2x :

9 = 1.8x

Divide both sides by 1.8:

x = \frac{9}{1.8} = 5

Thus, the walking speed is5 mph, so his jogging speed is:

2x = 2 \times 5 = 10

Therefore, his average jogging speed is10 mph.

Given that John jogged 5 miles and walked 2 miles, and that the total trip took 0.9 hours, we can set up the following equations for the time spent jogging and walking:

The total time is the sum of these two times:

To solve for

So,

Multiply both sides by

Divide both sides by 1.8:

Thus, the walking speed is

Therefore, his average jogging speed is

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