Question

A student on the track team runs 45 minutes each day as a part of her training. She begins her workout by running at a constant rate of 8 miles per hour for a minutes, then slows to a constant rate of 7.5 miles per hour for b minutes.



Which equation describes the relationship between the distance she runs in miles, D, and her running speed, in miles per hour?



8a+7.5b=D8a+7.5b=D

Answer 1

The equation that describes the relationship between the distance she runs in miles, $D$,and her running speed, $b$, in miles per hour is $D = 8(45 - b) + 7.5b$.

So, option $D$ is correct.

$\textup{Speed} = \frac{\textup{Distance}}{\textup{Time}}$

So, $\textup{Distance} = \textup{Speed} \times \textup{Time}$

She begins her workout by running at a constant rate of miles per hour for $a$ minutes, then slows to a constant rate of miles per hour for $b$ minutes.

$D=8 a + 7.5 b...(i)$

Also, $a+b=45$

So, $a=45-b$

Substitute the value of $a$ in $(i)$

$D=8 (45-b) + 7.5 b$

So, the correct equation is $D=8 (45-b) + 7.5 b$.

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