Question 171635
Two men start from the same corner "A", going in different directions around a field 1 mile square. The man going along AB walks 4 miles an hour, and the other man who is traveling AD goes 3 miles an hour. Where and after how long will they meet?
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The perimeter (ABCD) of the square = 4 mi
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The two men will have traveled a total distance of 4 mi when they meet.
there:
Let d = distance traveled by the 1st guy when they meet from "A"
Then
(4-d) = distance traveled by the 2nd guy when they meet
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The travel times of both men will be the same
Write time equation:  Time = {{{dist/speed}}}
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A's time = B's time
{{{d/4}}} = {{{(4-d)/3}}}
Cross multiply to find d
3d = 4(4-d)
3d = 16 - 4d
3d + 4d = 16
7d = 16
d = {{{16/7}}} miles traveled by the 1st guy
Which would put him between C & D, actually 2/7 mi from C
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Find the travel time of A, who is traveling 4 mph:
{{{16/7}}} * {{{1/4}}} = {{{4/7}}} hrs or 34.3 min
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Check solution using the 2nd man traveling 3 mph, find his distance (4-d)
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4 - {{{16/7}}} = {{{28/7}}} - {{{16/7}}} = {{{12/7}}} mi for the 2nd guy
That would put him between D & C, actually 5/7 mi from D
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Find the travel time of the 2nd guy who is traveling at 3 mph
{{{12/7}}} * {{{1/3}}} = {{{4/7}}} hrs or 34.3 min as it should be;
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Did this procedure make sense to you?