SOLUTION: . A train traveling at 50 miles per hour leaves for a certain town. Two hours later, a bus (starting at the same point as the train) traveling at 60 miles per hour leaves for the s

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Question 278190: . A train traveling at 50 miles per hour leaves for a certain town. Two hours later, a bus (starting at the same point as the train) traveling at 60 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 stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A train traveling at 50 miles per hour leaves for a certain town.
Two hours later, a bus (starting at the same point as the train) traveling at 60 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?
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Train DATA:
rate = 50 mph ; time = x hrs. ; distance = rt = 50x miles
------------------------------------------------------------
Bus DATA:
rate = 60 mph ; time = x-2 hrs ; distance = rt = 60(x-2) miles
--------------------------------------------------------------
Equation:
distance = distance
50x = 60(x-2)
50x = 60x - 120
-10x = -120
x = 12 miles
======================
Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A train traveling at 50 miles per hour leaves for a certain town.
Two hours later, a bus (starting at the same point as the train) traveling at 60 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?
:
Let d = distance between the towns
:
Write time equation: time = dist/speed
:
train travel time - bus travel time = 2 hrs
d%2F50 - d%2F60 = 2
:
Multiply equation by 300 to get rid of the denominators, results
6d - 5d = 2(300)
d = 600 miles between towns
:
:
Confirm this by finding the travel times of each
600/50 = 12 hrs
600/60 = 10 hrs