Answer:
18 + 22.5 = 40 + .5; confirms out solution
Explanation:
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
:
Let d = distance from x to y
:
Write a time equation; time = distance%2Fspeed
Different speed roundtrip time = 1 speed roundtrip time + half/hour
d%2F50 + d%2F40 = 2d%2F45 + 1%2F2
Multiply equation by 1800 to get rid of the denominators:
1800*d%2F50 + 1800*d%2F40 = 1800*2d%2F45 + 1800*1%2F2
Cancel the denominators and you have:
:
36d + 45d = 40(2d) + 900
:
81d = 80d + 900
:
81d - 80d = 900
:
d = 900 miles from x to y
:
:
Check solution in: d%2F50 + d%2F40 = 2d%2F45 + 1%2F2
900%2F50 + 900%2F40 = 1800%2F45 + 1%2F2
18 + 22.5 = 40 + .5; confirms out solution