SOLUTION: Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive eac

Question 158306: Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way.
(i'm in 8th grade, and it just doesn't make sense to me) But I think this is what I am supposed to do, but I don't understand why it works.. if it does.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Danielle drove from school to home averaging 20 mph. On the way back to school she averaged 30 mph. If the total driving time was 1.5 hours, how long did it take her to drive each way.
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School to home DATA:
rate = 20 mph ; distance = x miles ; time = d/r = x/20 hrs
---------------------------
home to school DATA:
rate = 30 mph ; distance = x miles ; time = d/r = x/30 hrs
-----------------------------
EQUATION:
time + time = 1.5 hours
x/20 + x/30 = 3/2
Multiply thru by 60 to get:
3x + 2x = 90
5x = 90
x = 18 miles (distance each way)
-----------
time to drive from home to school = 18/20 = 9/10 hr = 54 minutes
time to drive from school to home = 18/30 = 3/5 hr = 36 minutes
======================
Cheers,
Stan H.
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