Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 34 meters ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 meter per second, and the adults hobbled after them at a rate of 2 meters per second. Soon they were side-by-side. How long did that take? How far did the adults go?It took ____ seconds for the adults to go ____ meters and catch up to the kids.

Answer 1

From the question,

The equation for the distance covered by the kids is d = 1 t + 34

The equation for the distance covered by the adults is d = 2t

Now, when the adults caught up with the kids was when : 2 t = 1 t + 34

Solving this equation, we have 2 t - 1 t = 34

t = 34

since d= 2 t , when t = 34

d = 2 x 34 = 68

It took ___34_ seconds for the adults to go _68___ meters and catch up to the kids.​