Question

Question

Solve the real-world situation by using the substitution method.
Jen is riding her bicycle on a trail at the rate of 0.33 kilometer per minute. Michelle is 8
kilometers behind Jen when she starts traveling on the same trail at a rate of 0.43 kilometer
per minute. Let d represent the distance in kilometers the bicyclists are from the start of
the trail and t represent the time in minutes.
The system of equations
d = 0.33t + 8
d = 0.43t
can be used to represent this situation.
р.
How many minutes will it take Michelle to catch up to Jen? How far will they be from the
start of the trail? Use the substitution method to solve this real-world application.
Michelle will catch up to Jen in
of the trail.
minutes and they will be
km from the start

Answer 1

9514 1404 393

Answer:

• 80 minutes
• 34.4 km

Explanation:

Use the second equation to substitute for d in the first equation.

0.43t = 0.33t +8

Subtract 0.33t from both sides

0.10t = 8

Multiply by 10

t = 80 . . . . . . Michelle will catch Jen in 80 minutes

The distance traveled will be ...

d = 0.43t = 0.43×80 = 34.4 . . . . km

The girls will have traveled 34.4 km when they meet.