Math Word Problem — Ship and Anchor

Remember those word problems in high school or freshman college math class? Maybe you, like a lot of people, hated them. Maybe you liked them. If you are in the latter group, here’s one for you:

A ship is twice as old as the anchor was when the ship was as old as the anchor is. The sum of their two present ages is 42 years. How old is each?

You can email me for the answer, or you can solve it and post your answer and solution in the comments. I haven’t looked but I wouldn’t be surprised that you could find the answer and the solution somewhere on the internet. But that would be cheating.

  • Em Arde

    Let:

    S = age ship is
    Ai = age anchor is
    Aw = age anchor was when ship was age anchor is

    From the story:

    S + Ai = 42
    -> S = 42 – Ai [1]

    S = 2 x Aw [2]

    Aw = Ai – (S – Ai) [3]

    From [3]:

    Aw = Ai – S + Ai
    -> Aw = 2 x Ai – S [4]

    Sub [4] into [2]:

    S = 2 x (2 x Ai – S)
    -> S = 4 x Ai – 2S
    -> 3 x S = 4 x Ai [5]

    Sub [1] into [5]:

    3 x (42 – Ai) = 4 x Ai
    -> 126 – 3 x Ai = 4 x Ai
    -> 7 x Ai = 126
    -> Ai = 126 / 7
    => Ai = 18

    So, from [1], S = 42 – 18 = 24

    Thus, the ship is currently 24 and the anchor is 18

    END

    • TeeJaw

      Brilliant! Your immediate recognition that the present age of the ship must be twice the age the anchor was, led you down the right path.

  • Rich

    Yes, that’s how I solved the problem; I believe the objective was to solve the problem.

    I used the “iterative approach”, a valid and accepted method used in scientific endeavors. When the situation requires it, the next step would be to generalizem and (hopefully) develop a formula or set of equations for solving similar problems in the future. I did not see the need for a general solution for the problem, and am content to leave that task for those who are interested, or have a continuing need for such. Cheers, R.

  • Rich Davis

    The ship is [bleep] years old’ the anchor is [bleep] years old.

    Solved in about 6 minutes.

    R.

    • TeeJaw

      Your answer is correct, but what was your solution?

      • TeeJaw

        Rich never answered my reply and never gave his solution. I assume he plugged in various numbers until he found two that worked. You should be more interested in how to solve problems such as this. The answers are not always as easy to find by trial and error as this one is.