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

Question 33543: A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus traveling at 50 miles per hours 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?
Please help me I think the answer is 200 but I don't know how to set the problem up
Found 2 solutions by Cintchr, Earlsdon:
Answer by Cintchr(481) (Show Source): You can put this solution on YOUR website!

In this case, the distance for both is the same, so for our convenience the train's variables are in caps.

r=50
t= T-1 (it started an hour later)
R=40
T= this is what we will solve for

Solve for T

Subtract 50T

divide by -10

So if the Train takes 5 hours, the bus takes 4.

CHECK

and this IS the distance.
This is a duplicate of problem 33542

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
You can use the distance formula:
where: d = distance travelled, r = rate of travel (speed), and t = time of travel.
For the train:

1)
For the bus:

2)
The distance is the same in each case, so d1 = d2, therefore, we can set:

But the train travels one hour longer than the bus, so t1 = t2+1
Making this substitution, we get:
Simplify and solve for t2.
Subtract 40(t20 from both sides of the equation.
Divide both sides by 10.
Now substitute this into equation 2) and solve for d2:

miles.
The town is 200 miles from the starting point.
RELATED QUESTIONS
A train traveling at 40 miles per hour leaves for a certain town. One hour later, a bus... (answered by rfer,josmiceli)
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 50 miles per hour leaves for a certain town. Two hours later, a bus (answered by ptaylor)
A train traveling at 50 miles per hour leaves for a certain town. Two hours later, a... (answered by Edwin McCravy)
. A train traveling at 50 miles per hour leaves for a certain town. Two hours later, a... (answered by stanbon,ankor@dixie-net.com)
A train traveling 60 miles per hour leaves for a certain town. Two hours later, a car... (answered by stanbon)
A train traveling 60 miles per hour leaves for a certain town. Two hours later, a car... (answered by richwmiller)
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)