SOLUTION: A motorist driving 90 km/h can go from Midland to Shiloh in two hours less than a train that averages 75 km/h. How far apart are the two towns?

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Question 166796: A motorist driving 90 km/h can go from Midland to Shiloh in two hours less than a train that averages 75 km/h. How far apart are the two towns?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can use: d+=+rt for this problem, where:
d = distance traveled.
r = rate (speed) of travel.
t = time taken to travel distance d at a speed of r.
For the car, r = 90 km/h.
For the train, r = 75 km/h
d%5Bc%5D+=+90%28t-2%29 (t-2 because the car takes 2 hours less than the train).
d%5Bt%5D+=+75t The distance is the same for each, so...
d%5Bc%5D+=+d%5Bt%5D
90%28t-2%29+=+75t
90t-180+=+75t Subtract 75t from both sides.
15t-180+=+0 Add 180 to both sides.
15t+=+180 Divide both sides by 15.
t+=+12 Now substitute this into either one of the two distance equations.
For the car:
d%5Bc%5D+=+90%28t-2%29 Substitute t = 12.
d%5Bc%5D+=+90%2812-2%29
d%5Bc%5D+=+90%2810%29
d%5Bc%5D+=+900km.
For the train:
d%5Bt%5D+=+75t Substitute t = 12.
d%5Bt%5D+=+75%2812%29
d%5Bt%5D+=+900km.
The towns are 900 km. apart.