Question

Two friends race. The first friend gets a head start and runs at a steady rate of 0.20 miles per minute. The second friend waits 1 minute and then runs at a steady rate of 0.25 miles per minute. How long will it take for the second runner to catch up with the first?

Answer 1

Explanation:

In this problem we are expected to solve for the time taken for the second person to meet with the first.

given that

first person's speed=0.2mph

let time taken be= x

we know that

velocity= distance/time

0.2=distance/x

distance=0.2x----1

second person's speed= 0.25mpm

time taken=x-1

we know that

velocity= distance/time

0.25=distance/x-1

distance=0.25(x-1)

distance=0.25x-0.25-----2

equating equation 1 and 2 we have

0.2x=0.25x-0.25

0.2x-0.25=-0.25

-0.05x=-0.25

divide both sides by -0.05 we have

x=-0.25/-0.05

x=5

we know that the second person's time is described by

=x-1

=5-1=4min

The second person will catch up after 4 minutes