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

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?

Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~

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.

Solved.

---------------
See introductory lessons on Travel and Distance problems
    - Travel and Distance problems
    - Travel and Distance problems for two bodies moving in opposite directions
    - Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.

You will find the solutions of many similar problems there.

Read them and learn once for all from these lessons on how to solve simple Travel and Distance problems.

Become an expert in this area.

RELATED QUESTIONS
A train traveling at 40 MPH leaves for a certain town. One hour later a bus traveling at... (answered by ankor@dixie-net.com)

A train traveling at 40 mph leaves for a certain town. One hour later, a bus traveling... (answered by mananth)

a train traveling at 40 moh leaves a certain town. One hour later, a bus traveling at 50... (answered by brucewill)

A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus... (answered by rfer,josmiceli)

A freight train leaves town, traveling at 35 mph. One hour later a Passenger train... (answered by checkley79)

Train A leaves a station traveling at 40 mph. Six hours later, train B leaves the same... (answered by solver91311)

Train A leaves a station traveling at 40 mph. Six hours later, train B leaves the same... (answered by ikleyn)

A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus... (answered by Cintchr)

A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus... (answered by Cintchr,Earlsdon)