SOLUTION: Two train stations are 1250 km apart. At midnight, a passenger train and a freight train leave these stations and start towards each other. The passenger train travels 30km/h faste

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Question 1073138: Two train stations are 1250 km apart. At midnight, a passenger train and a freight train leave these stations and start towards each other. The passenger train travels 30km/h faster than the freight train, but the passenger train stops for one hour while the freight train travels non-stop. The two trains pass each other at 5:00. Find the rate of each train.
Found 3 solutions by ankor@dixie-net.com, MathTherapy, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
Two train stations are 1250 km apart. At midnight, a passenger train and a freight train leave these stations and start towards each other.
The passenger train travels 30km/h faster than the freight train, but the passenger train stops for one hour while the freight train travels non-stop.
The two trains pass each other at 5:00. Find the rate of each train.
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I am ashamed to say that I made a stupid math mistake. Here is the corrected version of this problem
:
let's assume the passenger train stops for 1 hr before they meet
then the passenger travel time = 4 hrs, the freight travels 5 hrs
let s = speed of the freight
then
(s+30) = the speed of the passenger train
The sum of their distances will be 1250 km
4(s+30) + 5s = 1250
4s + 120 + 5s = 1250
9s = 1250 - 120
9s = 1130
s = 1130/9
s = 125.6 km/hr is the speed of the freight
then
125.6 + 30 = 155.6 km/hr is the speed of the passenger train
:
Now let's assume the passenger train stops for 1 hr after they meet
then both the passenger and the freight travel for 5 hrs
let s = speed of the freight
then
(s+30) = the speed of the passenger train
The sum of their distances will be 1250 km
5(s+30) + 5s = 1250
5s + 150 + 5s = 1250
10s = 1250 - 150
10s = 1100
s = 1100/10
s = 110 km/hr is the speed of the freight
then
110 + 30 = 140 km/hr is the speed of the passenger train

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Two train stations are 1250 km apart. At midnight, a passenger train and a freight train leave these stations and start towards each other. The passenger train travels 30km/h faster than the freight train, but the passenger train stops for one hour while the freight train travels non-stop. The two trains pass each other at 5:00. Find the rate of each train.

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
Where or when the passenger train stops for an hour will not matter. The two trains are consuming the 1250 km distance between them.

TRAIN SPEED TIME DISTANCE PASSENGER r+30 4 (r+30)(4) FREIGHT r 5 (r)(5) Total 1250

Or to three signif. figures,
-----freight train speed
-----passenger train speed