Question 389394: 3 persons, namely A, B and C started from the same point on the same time to turn around the pond. The speed of A, B and C was 400m, 600m and 300m in per minute, and A turned counter clockwise, B and C turned clockwise. Then, A met C 3 minutes after A had met B. How many meters is the surrounding of the pond?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 3 persons, namely A, B and C started from the same point on the same time to turn around the pond.
The speed of A, B and C was 400m, 600m and 300m in per minute, and A turned
counter clockwise, B and C turned clockwise.
Then, A met C 3 minutes after A had met B. How many meters is the surrounding of the pond?
:
Summarize
A, 400m, CCw
B, 600m, CW
C, 300m, CW
:
Let d = distance around the pond
Let t = time for A to meet B
then
(t+3) = time for A to meet C
:
Write a distance equation for A meets B (dist = speed*time)
d = 400t + 600t
d = 1000t
:
Write a distance equation for A meeting C (3 min later)
d = 400(t+3) + 300(t+3)
d = 400t + 1200 + 300t + 900
d = 700t + 2100
Replace d with 1000t from the 1st equation
1000t = 700t + 2100
1000t - 700t = 2100
300t = 2100
t = 7 min for A to meet B
Find the dist
d = 1000(7)
d = 7000 meters around the pond
:
Confirm this by finding the distance using A meets C in 10 min
d = 10(400) + 10(300)
d = 4000 + 3000;
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