SOLUTION: 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

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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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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?
:
The perimeter (ABCD) of the square = 4 mi
:
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
:
The travel times of both men will be the same
Write time equation: Time = dist%2Fspeed
:
A's time = B's time
d%2F4 = %284-d%29%2F3
Cross multiply to find d
3d = 4(4-d)
3d = 16 - 4d
3d + 4d = 16
7d = 16
d = 16%2F7 miles traveled by the 1st guy
Which would put him between C & D, actually 2/7 mi from C
:
Find the travel time of A, who is traveling 4 mph:
16%2F7 * 1%2F4 = 4%2F7 hrs or 34.3 min
:
:
Check solution using the 2nd man traveling 3 mph, find his distance (4-d)
:
4 - 16%2F7 = 28%2F7 - 16%2F7 = 12%2F7 mi for the 2nd guy
That would put him between D & C, actually 5/7 mi from D
:
Find the travel time of the 2nd guy who is traveling at 3 mph
12%2F7 * 1%2F3 = 4%2F7 hrs or 34.3 min as it should be;
:
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Did this procedure make sense to you?