SOLUTION: Train A leaves a station traveling at 40 miles per hour. Four hours later train B leaves the same station traveling in the same direction at 60 miles per hour. How long does it tak

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Question 269091: Train A leaves a station traveling at 40 miles per hour. Four hours later train B leaves the same station traveling in the same direction at 60 miles per hour. How long does it take for train B to catch up to train A?
[A] 9 hr [B]10hr [C] 8hr [D] 11hr

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What is A's headstart?
d+=+r%2At
d+=+40%2A4
d+=+160 mi
Now you start a stopwatch. The start time and stop time
for both trains will be the same, or t%5Ba%5D+=+t%5Bb%5D
so call this time t
(1) d%5Ba%5D+=+r%5Ba%5D%2At
(2) d%5Bb%5D+=+r%5Bb%5D%2At
given:
r%5Ba%5D+=+40
r%5Bb%5D+=+60
So, now I have:
(1) d%5Ba%5D+=+40t
(2) d%5Bb%5D+=+60t
Train B has to make up the 160 mi headstart of train A, so
d%5Bb%5D+=+d%5Ba%5D+%2B+160
So, I have:
(1) d%5Ba%5D+=+40t
(2) d%5Ba%5D+%2B+160+=+60t
Substitute (1) into (2)
40t+%2B+160+=+60t
20t+=+160
t+=+8
It takes 8 hrs for B to catch A
check:
(1) d%5Ba%5D+=+40t
d%5Ba%5D+=+40%2A8
d%5Ba%5D+=+320
(2) d%5Bb%5D+=+60t
d%5Bb%5D+=+60%2A8
d%5Bb%5D+=+480
d%5Bb%5D+-+d%5Ba%5D+=+480+-+320
480+-+320+=+160
That was headstart of A