a man travels from town X to town Y at an average rate of 50 miles an hour and returns at an average rate of 40 miles an hour he takes a half hour longer than he would take if he made round trip at an average 45 miles an hour what is the distance from town X to town y

18 + 22.5 = 40 +.5; confirms out solution

Step-by-step 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