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
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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(52824) (Show Source):
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.
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
