SOLUTION: A train traveling in a southerly direction at 40 mph leaves for Happy Town. One hour later, a bus traveling in a northerly direction at 50 mph leaves for Happy Town and arrives at
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Question 1115135: A train traveling in a southerly direction at 40 mph leaves for Happy Town. One hour later, a bus traveling in a northerly direction at 50 mph leaves for Happy Town and arrives at the same time as the train. The distance between the two starting points is 400 miles. For how long did the train travel? How long did the bus travel? How far is the town from where they started?
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A train traveling in a southerly direction at 40 mph leaves for Happy Town.
One hour later, a bus traveling in a northerly direction at 50 mph leaves for Happy Town and arrives at the same time as the train.
The distance between the two starting points is 400 miles.
For how long did the train travel? How long did the bus travel? How far is the town from where they started?
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Let "t" be the time the train traveled, in hours.
Then the bus traveled one hour less time, (t-1) hours.
The train traveled 40*t miles.
The bus traveled 50*(t-1) miles.
Together, the two distances are 400 miles:
40t + 50*(t-1) = 400.
40t + 50t - 50 = 400
90t = 400 + 50 = 450 ====> t = = 5 hours.
Thus we founded that the train traveled 5 hours.
Hence, the bus traveled 5-1 = 4 hours.
The train traveled 40*5 = 200 miles.
The bus traveled 50*4 = 200 miles.
