SOLUTION: Ben has to go to soccer practice. He and his brother leave their house and drive to the school averaging 50 miles per hour. On the way home they averaged only 30 miles per hour due

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Question 446733: Ben has to go to soccer practice. He and his brother leave their house and drive to the school averaging 50 miles per hour. On the way home they averaged only 30 miles per hour due to traffic. What was the average speed of the trip? The answer is NOT 40 miles per hour.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
He and his brother leave their house and drive to the school averaging 50 miles per hour.
On the way home they averaged only 30 miles per hour due to traffic.
What was the average speed of the trip?
:
Let a = average speed for the round trip
:
Let d = one-way distance to school
;
Write time equation: time = dist/speed
:
To time + return time = total time
d%2F50 + d%2F30 = %282d%29%2Fa
Multiply by 150a to clear the denominators
150a*d%2F50 + 150a*d%2F30 = 150a*%282d%29%2Fa
cancel the denominators
3a(d) + 5a(d) = 150(2d)
Divide thru by d, we don't need that
3a + 5a = 150(2)
8a = 300
a = 300%2F8
a = 37.5 mph is the average speed for the round trip
:
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You can confirm this. Use a one-way dist of 150 mi
150/50 + 150/30 = 300/37.5