Question

A man travels from town X to town Y at an average rate of 60 mph and returns at an average rate of 50 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 55 mph. What is the distance from Town X to Town Y?

Answer 1

1650 miles

Explanation:

Answer 2

Distance = d miles ; rate = 60 mph ; time = d/60 hrs

distance = d miles ; rate = 50 mph ; time = d/50 hrs
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Round-trip DATA:
distance = 2d miles ; rate = 55 mph ; time = (2d)/55 hrs
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Equation:

Roundtrip time - other time = -1/2 hr
(2d)/55 - [(d/60)+(d/50)] = -1/2
(2d)/55 - [(110d)/(50*60)] = -1/2
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600(2d) - 11[110d] = -16500
1200d - 1210d = -16500
-10d = -16500
distance = 1650 miles

Hope this helped :)