SOLUTION: A freight train and a passenger train are in stations 540km apart. The freight train leaves the station at noon travelling at 60km/hr in the direction of the passenger train . One

Question 1097682: A freight train and a passenger train are in stations 540km apart. The freight train leaves the station at noon travelling at 60km/hr in the direction of the passenger train . One hour later, the passenger train leaves and heads towards the freight train at 90km/h. At what time will the two trains meet.
I know why one of the equation is 540 = 60x + 90y, but I don't understand why the other equation is x=y+1. Please help me understand.
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
This analysis is changed slightly to use just one variable. The passenger train traveled here for x hours and freight train traveled just one hour longer.

SPEED TIME DISTANCE Freight 60 x+1 60(x+1) Passenger 90 x 90x Total 540

You have just a single equation to solve:

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
A freight train and a passenger train are in stations 540km apart.
The freight train leaves the station at noon travelling at 60km/hr in the direction of the passenger train .
One hour later, the passenger train leaves and heads towards the freight train at 90km/h. At what time will the two trains meet.
I know why one of the equation is 540 = 60x + 90y, but I don't understand why the other equation is x=y+1. Please help me understand.
~~~~~~~~~~~~~~~~~~

You are on correct track. First equation is 540 = 60x + 90y, because one train covered 60x kilometers, while the second covered 90y kilometers, and together these two distances are exactly 540 km. The second equation is x = y+1, BECAUSE the freight train started in 1 hour earlier (before) than the passenger train, and, therefore, the freight train was on his way in one hour longer than the passenger train, before they meet each other. Hope, this explanation will help you.

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See the lesson
    - Travel and Distance problems
    - Travel and Distance problems for two bodies moving in opposite directions
in this site.

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

A freight train and a passenger train are in stations 540km apart. The freight train leaves the station at noon travelling at 60km/hr in the direction of the passenger train . One hour later, the passenger train leaves and heads towards the freight train at 90km/h. At what time will the two trains meet.
I know why one of the equation is 540 = 60x + 90y, but I don't understand why the other equation is x=y+1. Please help me understand.

First of all, it's obvious that you let "x" and "y" be the times that the freight and passenger trains took, respectively, to get to the catch-up point.
Now, since the freight train left one hour before the passenger train, and therefore took 1 hour more than the passenger train, to get to the catch-up point,
the TIME equation formed is: Time taken by freight train = Time taken by passenger train, plus 1, OR
x = y + 1
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