SOLUTION: Two passenger trains started at the same time from towns 288 miles apart and met in 3 hours. The rate of the one train was 6 miles per hour slower than that of the other. Find the

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Question 1094059: Two passenger trains started at the same time from towns 288 miles apart and met in 3 hours. The rate of the one train was 6 miles per hour slower than that of the other. Find the rate of each train.
Found 2 solutions by addingup, greenestamps:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
rate of one train: x
rate of the other: x-6
time: 3
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3x+3(x-6) = 288
3x+3x-18 = 288
3x+3x = 306
6x = 306
x = 51 miles per hour. This is the rate of one train
x-6 = 51-6 = 45 mph. This is the rate of the other train

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

The trains together cover 288 miles in 3 hours, so their combined speed is
288%2F3+=+96

The speed of one train is 6 mph slower than the other; so you need two speeds that differ by 6 and add to 96. If we use f and s for the speeds of the fast and slow trains, then we could use formal algebra and say
f%2Bs+=+96
f-s+=+6
2f+=+102 (add the two equations, to eliminate s)
f+=+51
s+=+96-f+=+45

Once I got the combined speed of96 for the two trains,I would be much less formal than that in solving the problem. I would simply "take away" the 6 "extra" mph of the faster train, leaving me with two trains going the same speed, and now with a combined speed of 96-6=90 mph. That would make the slower train going 90/2=45 mph, which means the fast train is going 45+6=51 mph.