Question

Sharlee can bicycle 52 miles in the same time as it takes her to walk 20 miles. She can ride 8 mph faster than she can walk. How fast can she walk?

Answer 1

To determine the walking speed, we set up equations using the rate-time-distance relationship and solved for w. Sharlee can walk at a speed of 5 mph.

Step-by-step explanation:

The student asks about determining the walking speed of a person, given that they can bicycle at a certain rate faster over respective distances. To solve this, we will use the concepts of rate, time, and distance. Let's denote the walking speed as w mph (miles per hour). Therefore, the bicycling speed will be w + 8 mph. Since the time taken for both activities is the same, we can set up the following equations based on the formula distance = rate × time:

Dividing the first equation by the second one, we get:

• Bicycling: 52 = (w + 8)t

• Walking: 20 = wt

52/(w + 8) = 20/w

Solving this equation for w gives us the walking speed. We can cross-multiply to simplify:

52w = 20(w + 8)

52w = 20w + 160

32w = 160

w = 160/32

w = 5

So, Sharlee walks at 5 mph.