# Thread: Variation on the "Two Trains" puzzle type

1. ## Variation on the "Two Trains" puzzle type

Two trains leave their stations heading to each other's starting station, travelling on parallel tracks in opposite directions. After the two trains cross paths, the first train takes one hour to reach it's destination, whilst the second train takes four hours to reach it's destination.

How much faster was the first train travelling in relation to the second train?

I've done a little model in Excel and it seems the answer is 2 times, but I'd like a formulaic solution to the problem.

2. Originally Posted by pajr777
Two trains leave their stations heading to each other's starting station, travelling on parallel tracks in opposite directions. After the two trains cross paths, the first train takes one hour to reach it's destination, whilst the second train takes four hours to reach it's destination.
I've done a little model in Excel and it seems the answer is 2 times, but I'd like a formulaic solution to the problem.
Correct.

y = speed 1st train, x = speed 2nd train, a = time paths crossed

When paths crossed:
1st train travelled ay, 2nd train travelled ax
After paths crossed:
1st train travelled y, 2nd train travelled 4x

So ay = 4x ; a = 4x / y
And ax = y ; a = y / x

4x / y = y / x
y^2 = 4x^2
y = 2x

3. Originally Posted by Wilmer
Correct.

y = speed 1st train, x = speed 2nd train, a = time paths crossed

When paths crossed:
1st train travelled ay, 2nd train travelled ax
After paths crossed:
1st train travelled y, 2nd train travelled 4x

So ay = 4x ; a = 4x / y
And ax = y ; a = y / x

4x / y = y / x
y^2 = 4x^2
y = 2x

Thank you so much, that is perfect