Solution to Shipping Algebra Puzzle

Last week I provided a logic puzzle about shipping and algebra. You can find the puzzle here.
Thanks to all those who sent a solution. Dan W and jeffem were right—the ship’s age is 24 and the boiler’s age is 18.

Here’s the algebra I used in my solution to the problem:
Let s = current age of ship, b = current age of boiler, and y = years passed since the age of the ship was equal to the current age of the boiler. You can translate the statements in the puzzle to the following three equations:

1) s + b = 42
2) s = 2*(b - y)
3) s - y = b

From equations 2 and 3 you get the equation:

s = 2*(b - s + b)

This gives us equation 4:

4) 3*s = 4*b

From equations 1 and 4 you get the equation:

3*s = 4*(42 - s)

When you solve the equation for s, you get 24. And now that the age of the ship is known, you can solve equation 1 for b:

b = 42 - 24 = 18

The solution is that the ship’s current age is 24 and the boiler’s is 18.


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