SOLUTION: 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 a

Question 298487: 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 by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
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To-trip DATA:
distance = d miles ; rate = 60 mph ; time = d/60 hrs
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From-trip DATA:
distance = d miles ; rate = 50 mph ; time = d/50 hrs
----------------------
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
---
600(2d) - 11[110d] = -16500
1200d - 1210d = -16500
-10d = -16500
distance = 1650 miles
===========================
Cheers,
Stan H.
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