SOLUTION: When Caitlin starts running towards Asha, Asha is 100 meters from Caitlin. As Caitlin runs, Asha moves directly away from Caitlin at one-third of Caitlin�s speed. How far has Caitl

Question 266995: When Caitlin starts running towards Asha, Asha is 100 meters from Caitlin. As Caitlin runs, Asha moves directly away from Caitlin at one-third of Caitlin�s speed. How far has Caitlin run when she first catches up to Asha?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
When Caitlin starts running towards Asha, Asha is 100 meters from Caitlin.
As Caitlin runs, Asha moves directly away from Caitlin at one-third of Caitlin�s speed.
How far has Caitlin run when she first catches up to Asha?
:
Briefly, C has to run 100 m more than A in the same amt of time
:
Let s = A's running speed
then
3s = C's running speed
:
Let d = distance run by A
then
(d+100) = distance run by C
:
Write a time equation: Time = dist/speed
:
C's running time = A's running time
=
Cross multiply
s(d+100) = 3s(d)
sd + 100s = 3sd
:
Divide thru by s and you have:
d + 100 = 3d
100 = 3d - d
100 = 2d
d = 50m is the distance run by A
then
50 + 100 = 150m is the distance run by C to catch A
:
Check this, assume A's speed is 10 m/sec, C's speed is 30 m/sec
Check the times of each, they should be equal
150/30 = 5 min
50/10 = 5 min
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