Question

Denise bikes 3 miles to her friend's house, and then she bikes home. The average rate biking to her friend's house is twice the average rate coming home. Write and simplify an expression for the time it takes Denise to make a round-trip in terms of the average rate coming home x. Hint : Use d = rt.

Answer 1

Using the relation between velocity, distance and time, it is found that the expression for the total time is given by:

$t = \frac{9}{2x}$

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

$v = \frac{d}{t}$.

Denise bikes 3 miles to her friend's house, hence:

$v_1 = \frac{3}{t_1}$

$t_1 = \frac{3}{v_1}$

The average rate biking to her friend's house is twice the average rate coming home, hence, on the return, $v_2 = 0.5v_1$:

$v_2 = \frac{3}{t_2}$

$t_2 = \frac{3}{v_2}$

$t_2 = \frac{3}{0.5v_1}$

$t_2 = \frac{6}{v_1}$

The total time is given by, considering $v_1 = 2v_2 = 2v = 2x$, as we want to consider x the rate coming home:

$t = t_1 + t_2$

$t = \frac{3}{2x} + \frac{6}{2x}$

$t = \frac{9}{2x}$

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

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