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 minutes, then slows to a constant rate of 7.5 miles per hour for minutes. which equation describes the relationship between the distance she runs in miles, , and her running speed, in miles per hour?

Answer 1

The equation for the distance is:

(a/60) × 8 mi/min + (b/60) × 7.5 mi/min = D

We know that she runs 45 minutes each day, such that she runs at a rate of 8 miles per hour for a minutes, and then runs at 7.5 miles per hour for b minutes.

Now, remember the relation:

speed × time = distance.

Because a and b are in minutes, we need to rewrite the speed in minutes, remember that there are 60 minutes in one hour, then:

8 mi/h = (1/60) × 8mi/min

7.5 mi/h = (1/60) × 7.5 mi/min

Then the equation for the distance is:

a × (1/60) × 8 mi/min + b × (1/60) × 7.5 mi/min = D

(a/60) × 8 mi/min + (b/60) × 7.5 mi/min = D

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