Question 446733
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? 
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Let a = average speed for the round trip
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Let d = one-way distance to school
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Write time equation: time = dist/speed
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To time + return time = total time
{{{d/50}}} + {{{d/30}}} = {{{(2d)/a}}}
Multiply by 150a to clear the denominators
150a*{{{d/50}}} + 150a*{{{d/30}}} = 150a*{{{(2d)/a}}}
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 = {{{300/8}}}
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