SOLUTION: Allison drove home at 66 mph, but her brother Austin, who left at the same time, could drive at only 52 mph. When Allison arrived, Austin still had 42 miles to go. How far did Alli

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Allison drove home at 66 mph, but her brother Austin, who left at the same time, could drive at only 52 mph. When Allison arrived, Austin still had 42 miles to go. How far did Alli      Log On

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Question 1174120: Allison drove home at 66 mph, but her brother Austin, who left at the same time, could drive at only 52 mph. When Allison arrived, Austin still had 42 miles to go. How far did Allison drive?
Found 3 solutions by Boreal, ewatrrr, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
She was 14 mph faster and beat him by 42 miles, so she drove 3 hours
-
distance is speed*time
time is x for Allison
distance is 66x
that equals 52x+42 for Austin
66x=52x+42
14x=42
x=3 hours
distance is 198 miles
in 3 hours, Austin drove 156 miles, which is 42 miles fewer.
198 miles.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,

Allison - 66mi/hr and Austin- 52mi/hr 
When Allison arrived, Austin still had 42 miles to go  0r 42/52 hrs to go

  66t = 52(t + 42/52)

  14t = 42

   t = 3hr

Allison had driven (66mi/hr)(3hrs) = 198mi

Wish You the Best in your Studies.


Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.

Another possible way to solve the problem is to use the "time" equation. 


Let d be the distance under the question.


Then you have this "time" equation


    d%2F66 = %28d-42%29%2F42.


To solve it, cross-multiply, then simplify


    42d = 66*(d-42)

    42d = 66d - 66*42

    66*42 = 66d - 42d

    66*42 = 14d

      d   = %2866%2A42%29%2F14 = 66*3 = 198 miles.    ANSWER

If you go this way, making equation is easy;
its solving is easy, too.

Another advantage is that you go straight way to your unknown quantity.


Solved.