SOLUTION: The speed of a passenger train is 14 mph faster than the speed of a freight train. The passenger train travels 270 miles in the same time it takes the freight train to travel 200

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Question 344588: The speed of a passenger train is 14 mph faster than the speed of a freight train. The passenger train travels 270 miles in the same time it takes the freight train to travel 200 miles. Find the speed of each train.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Rate*Time=Distance
.
.
R%2At=D
1.R%5Bp%5D%2At=270
2.R%5Bf%5D%2At=200
3.R%5Bp%5D=R%5Bf%5D%2B14
Substitute eqs. 1 and 2 into eq. 3,
From eq. 1,
t=270%2FR%5Bp%5D
From eq. 2,
t=200%2FR%5Bf%5D
Set them equal to each other,
270%2FR%5Bp%5D=200%2FR%5Bf%5D
270%2AR%5Bf%5D=200%2AR%5Bp%5D
R%5Bf%5D=%2820%2F27%29%2AR%5Bp%5D
Substitute into eq. 3,
R%5Bp%5D=%2820%2F27%29%2AR%5Bp%5D%2B14
R%5Bp%5D%281-20%2F27%29=14
R%5Bp%5D%2827%2F27-20%2F27%29=14
R%5Bp%5D%287%2F27%29=14
R%5Bp%5D=%2827%2A14%29%2F7
highlight%28R%5Bp%5D=54%29mph
Then from eq. 3,
highlight%28R%5Bf%5D=40%29mph