Question

A couple of friends decide to race each other. Emmet can run 6 yards per second, whereas Ayana can run 9 yards per second. Because he is slower, Emmet also gets a head start of 30 yards. Shortly after they start running, Ayana will catch up to Emmet. How far will Ayana have to run?Write a system of equations, graph them, and type the solution.

Answer 1

We know the formula d=rt where d is distance, r is rate and t is time

Emmet:

d = 6 yd/s * t

Ayana:

d = 9 yd/s * t

We give Emmet 30 less yards to run

Emmet:

d - 30 = 6 yd/s * t

d = 6t + 30

Setting the equations equal to each other

9 * t = 6t + 30

Subtract 6t from each side

9t-6t = 30

3t = 30

Divide by 3

3t/3 = 30/3

t = 10 seconds

It will take 10 seconds for Ayana to catch up

Ayana:

d = 9 yd/s * t

d = 8 * 10 = 90 yds