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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=70t

{s=t+1/2

for t to find the value of s, the number of hours Stephanie will have driven before Tina catches up to her.

Answer 1

Distance = rate x time: D = R * T

Rate = speed (miles per hour)

Since Stephanie starts a half an hour earlier, you need to calculate this distance as 56(.5) = 28 miles.

After this 28 miles, the time that both Stephanie and Tina travel is the same, so we only need one variable for time: t

D_stephanie + 28 miles = D_Tina

R_Stephanie * t + 28 = R_Tina * t

Equation to solve: 56t + 28 = 70t

Subtract 56t from both sides: 28 = 70t - 56t = 14t;

28 = 14t

Divide both sides by 14: t = 2 hours before Tina catches Stephanie

Tina's distance = 70 * 2 = 140 miles at the point where she catches Stephanie