SOLUTION: Allison drove home at 70 mph, but her brother Austin, who left at the same time, could drive at only 54 mph. When Allison arrived, Austin still had 48 miles to go. How far did Alli

Question 1121635: Allison drove home at 70 mph, but her brother Austin, who left at the same time, could drive at only 54 mph. When Allison arrived, Austin still had 48 miles to go. How far did Allison drive?
Found 2 solutions by ikleyn, solver91311:
Answer by ikleyn(52818)   (Show Source): You can put this solution on YOUR website!
.

Let t be the time they drove. Then you have this "distance" equation 70*t = 54*t + 48, saying that both parts of the equation represent the same distance. Then 70t - 54t = 48, 16t = 48 ====> t = 48/16 = 3 hours. Hence, the distance is 3*70 = 210 miles.

Solved.

There are other ways to solve the problem, but this one is the simplest, probably.

---------------

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Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Distance equals rate times time, so Allison's trip is modeled by while Austin's trip is modeled by . We can use the same in each model because the time of travel is given as the same.

But we know that , so

Which is to say:

But that means

Solve for , then calculate

John

My calculator said it, I believe it, that settles it

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