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Inga [223]
4 years ago
11

One runner passes another runner traveling in the same direction on a hiking trail. the faster runner is jogging 4 miles per hou

r faster than the slower runner. determine how long it will be before the faster runner is five eighths mile ahead of the slower runner.
Mathematics
1 answer:
Rus_ich [418]4 years ago
4 0

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

\text{fast runner: } s_f = v_ft,\quad \text{slow runner: } s_s = v_st

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

s_f-s_s = v_ft-v_st = (v_f-v_s)t

Now we plug in the fact that the faster speed is four more than the slower speed, i.e. v_f = v_s+4. The equation for the difference becomes

s_f-s_s = (v_f-v_s)t = (v_s+4-v_s)t = 4t

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

\cfrac{5}{8} = 4t

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

\cfrac{5}{32} = t

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

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Answer:

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<u>Pre-Algebra</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

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  3. Multiply:                               f(3) = 27 + 6 - 3
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