Question

User

A triathlete is training for the swimming and running portions of an upcoming triathlon.
She plans to swim and run a total of 10 miles today. She begins at the end of a jetty that extends out into the ocean and swims at an angle toward the beach, aiming for a point that she has estimated will make her time swimming and
0.5 mi
running approximately the same. Her expected rate of swimming is 2 mi/h and her expected rate of running is 8 mi/h. For what value of x will her time swimming and her time running be equal?

Answer 1

The triathlete should swim for 2 miles in order to have equal times swimming and running because her swimming rate is 2 mi/h and her running rate is 8 mi/h.

Step-by-step explanation:

The student triathlete needs to determine for what value of x will her time swimming and her time running be equal. Given her swimming rate is 2 mi/h and her running rate is 8 mi/h, we can set up the following equation where x is the distance swum:

Time swimming = x / 2 mi/h
Time running = (10 - x) / 8 mi/h

To find when the times are equal, we set the equations equal to each other:

x / 2 = (10 - x) / 8

Multiplying both sides by 8 to eliminate the denominator, we get:

4x = 10 - x

Adding x to both sides yields:

5x = 10

Dividing by 5 results in:

x = 2 miles

The student triathlete should swim 2 miles to have equal times swimming and running.