SOLUTION: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 14 miles per hour slower than the eastbound train. If the two trains

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Question 1151248: Two trains leave the station at the same time, one heading west and the other east. The westbound train travels 14 miles per hour slower than the eastbound train. If the two trains are 900 miles apart after 5 hours, what is the rate of the westbound train? Don't do any rounding. Urgent!
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let east bound train (A) speed =x mph
west bound train(B) speed will be x-14 mph.

Distance+=+speed+%2A+time
distance traveled by train A =+5x
distance traveled by train B = 5%2A%28x-14%29
5x%2B5%28x-14%29=900
5x%2B5x-70+=900
10x=900%2B70
10x=970
x=97 mph => speed of east bound train
the rate of the westbound train is: x-14=97-14=highlight%2883%29 mph

check:
distance between trains after 5h
train A: d=97%28mil%2Fh%29%2A5h=485mil
train B:d=83%28mil%2Fh%29%2A5h=415mil
distance between:485%2B415=900 mil

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The combined rate of the two trains is 900/5 = 180mph.

So you need two rates with a sum of 180, with one rate 14mph slower than the other.

From here, you can solve the problem with simple algebra:

x+%2B+%28x-14%29+=+180
2x-14+=+180
2x+=+194
x+=+97

The two rates are x=97 mph and x-14 = 83 mph.

If an algebraic solution is not required, here is a quick way to find the two rates with some simple arithmetic.

The sum of the two rates is 180.
If the two rates were the same, they would be 90 and 90.
To get two rates with the same sum but a difference of 14, add 7 to one rate and subtract 7 from the other.

ANSWER: The two rates are 90+7 = 97mph and 90-7 = 83mph.