<PRE><B>Question 124186</B>
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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Let d = distance from x to y
:
Write a time equation; time = {{{distance/speed}}}
Different speed roundtrip time =  1 speed roundtrip time + half/hour
{{{d/50}}} + {{{d/40}}} = {{{2d/45}}} + {{{1/2}}}
Multiply equation by 1800 to get rid of the denominators:
1800*{{{d/50}}} + 1800*{{{d/40}}} = 1800*{{{2d/45}}} + 1800*{{{1/2}}}
Cancel the denominators and you have:
:
36d + 45d = 40(2d) + 900
:
81d = 80d + 900
:
81d - 80d = 900
:
d = 900 miles from x to y
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:
Check solution in: {{{d/50}}} + {{{d/40}}} = {{{2d/45}}} + {{{1/2}}}
{{{900/50}}} + {{{900/40}}} = {{{1800/45}}} + {{{1/2}}}
    18 + 22.5 = 40 + .5; confirms out solution
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