One runner passes another runner traveling in the same direction on a hiking trail. the faster runner is jogging 4 miles per hour faster than the slower runner. determine how long it will be before the faster runner is five eighths mile ahead of the slower runner.

Both runners are running at a constant speed. Say that the fastest runner goes at speed (for fast) and the slowest goes at speed (for slow).

Let's start the observation at the moment of the passing: the two runners are in the exact same position. The laws that determine their position in the future are

This means that the difference between the two positions is given by

Now we plug in the fact that the faster speed is four more than the slower speed, i.e. . The equation for the difference becomes

And we want this difference to be 5/8 miles, so the request is

To solve for t, divide both sides by 4 to get

So, after 5/32 of a hour the two runners will be at 5/8 miles from each other.

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step-by-step explanation: