Mathematics, 14.07.2019 04:00 Willywill15

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.

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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.

Answer from: Quest

answer set (b) 0.5, 3/4 80% is in order from least to greatest.

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form. typically, the best form in which to evaluate rational numbers is in decimals. in order to convert a percent to a decimal, you would divide the given percentage by 100. you can also accomplish the conversion by moving the decimal point over two places to the left. for example, the decimal value of 80% is 80/100, or 0.8. in order to convert a fraction to a decimal, you need to divide the numerator by the denominator. for example, 3/4 is 0.75. so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.

Answer from: Quest

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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