Question

Stephanie left Riverside, California, driving her motorhome north on Interstate 15 towards Salt Lake City at a speed of 56 miles per hour. Half an hour later, Tina left Riverside in her car on the same route as Stephanie, driving 70 miles per hour. Solve the system {56s=70ts=t+12 for t to find the value of s, the number of hours Stephanie will have driven before Tina catches up to her.

Answer 1

The number of hours Stephanie will have driven before Tina catches up to her is 2.5 hours

Explanation:

Given:

56s=70t

s=t+1/2

Solution

56s=70t

s=t+1/2

Substitute s=t+1/2 into 56s=70t

56s=70t

56(t+1/2)=70t

56t+28=70t

28=70t - 56t

28=14t

Divide both sides by 14

28/14=14t/14

2=t

t=2

Recall,

s=t+1/2

s=2+1/2

=4+1/2

s=5/2

Or

s=2.5 hours