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

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) (Show Source): You can put this solution on YOUR website!
rate of one train: x
rate of the other: x-6
time: 3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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(13209) (Show Source): You can put this solution on YOUR website!

The trains together cover 288 miles in 3 hours, so their combined speed is

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

(add the two equations, to eliminate s)

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.
RELATED QUESTIONS
A freight train and a passenger train start toward each other at the same time from two... (answered by ankor@dixie-net.com)
two trains started from the same place at the same time and traveled in opposite... (answered by oscargut)
two trains started from the same place @ the same time and travel in oppisite directions. (answered by mananth)
Two trains leave towns 1332 km apart at the same time and travel toward each other. One... (answered by rfer)
Two trains leave towns apart at the same time and travel toward each other. One train... (answered by Alan3354)
Two trains leave towns 324 mi apart at the same time and travel toward each other. One... (answered by solver91311)
Two trains leave towns 915 mi apart at the same time and travel toward each other. One... (answered by stanbon)
Two trains leave towns 614km apart at the same time and travel toward each other. One... (answered by Edwin McCravy)
Two trains leave towns 1084km apart at the same time and travel toward each other. One... (answered by ikleyn)