SOLUTION: Allison drove home at 68 mph, but her brother Austin, who left at the same time, could drive at only 44 mph. When Allison arrived, Austin still had 120 miles to go. How far did All

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Question 1164009: Allison drove home at 68 mph, but her brother Austin, who left at the same time, could drive at only 44 mph. When Allison arrived, Austin still had 120 miles to go. How far did Allison drive?
Found 3 solutions by solver91311, MathTherapy, greenestamps:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


One drove miles at in some amount to time, . So:




The other drove miles at in the same amount to time, . So:



Since the time is the same:



Solve for

John

My calculator said it, I believe it, that settles it
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Allison drove home at 68 mph, but her brother Austin, who left at the same time, could drive at only 44 mph. When Allison arrived, Austin still had 120 miles to go. How far did Allison drive?
Let distance Allison drove (distance home), be D

Then distance Austin drove, was D - 120

Then we get the following TIME equation: 

 ------ Factoring out GCF, 4, in denominator

11D = 17(D - 120)

11D = 17D - 17(120)

11D - 17D = - 17(120)

- 6D = - 17(120)

Distance Allison drove, or  

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


You have received two perfectly good formal algebraic solutions using
          distance
  time = ----------
           speed


When the times are the same, many problems like this can be solved much more easily using this:
          DIFFERENCE IN distances
  time = -------------------------
           DIFFERENCE IN speeds


The difference in their speeds was 24mph; the difference in distance traveled was 120 miles.


Therefore, the time driving was 120/24 = 5 hours.


So the distance Allison drove was 5*68 = 340 miles.


 

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