SOLUTION: A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus traveling at 50 miles per hour leaves for the same town and arrives at the same time as the

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Question 205730: A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus traveling at 50 miles per hour leaves for the same town and arrives at the same time as the train. If both the train and the bus traveled in a straight line, how far is the town from where they started?
Found 2 solutions by rfer, josmiceli:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
The bus gains on the train at 10 mph, the train is 40 mi ahead of the bus, so it will take the bus 4 hrs to catch the train.
4*50=200 mi distance

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!

I will write 2 equations, 1 for the bus and 1 for the train
d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D
and
d%5Bt%5D+=+r%5Bt%5D%2At%5Bt%5D
-------------
given:
r%5Bb%5D+=+50 mi/hr
r%5Bt%5D+=+40 mi/hr
t%5Bt%5D+=+t%5Bb%5D+%2B+1
d%5Bb%5D+=+d%5Bt%5D (I'll call them both d)
----------------
d+=+50%2At%5Bb%5D
d+=+40%2A%28t%5Bb%5D+%2B+1%29
d+=+40t%5Bb%5D+%2B+40
I'll subtract these equations
d+=+50t%5Bb%5D
-d+=+-40t%5Bb%5D+-+40
0+=+10t%5Bb%5D+-+40
10t%5Bb%5D+=+40
t%5Bb%5D+=+4 hr
Now I'll solve for d
d+=+50t%5Bb%5D
d+=+50%2A4
d+=+200 mi
The town is 200 mi from where they started
check answer:
d+=+40t%5Bb%5D+%2B+40
200+=+40%2A4+%2B+40
200+=+160+%2B+40
200+=+200
and
t%5Bt%5D+=t%5Bb%5D+%2B+1
t%5Bt%5D+=+4+%2B+1
t%5Bt%5D+=+5 hr
d+=+40t%5Bt%5D
200+=+40%2A5
200+=+200
OK