A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rate of 40 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y?
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Given:
Average rate of man when travelling to town Y from town X = 50 mph
Average rate of his return = 40 mph
When average rate of the round trip = 45 mph then time taken i 1/2 hour more.
To find:
Distance from Town X to Town Y.
Solution:
Let the distance between Town X and Y be d.
We know that time = speed/ distance
The equation of time will be :
d/ 50 + d/ 40 = 2d/45 + 1/2
d/50 + d/40 - 2d/45 = 1/2
The L.C.M of the denominators will be 1800. Therefore:
[36d + 45d - (2*40)] / 1800 = 1/2
d / 1800 = 1/2
d = 1800 / 2
d = 900 miles
Therefore the distance between town X and town y will be 900 miles.
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