Gifted Issues Discussion homepage Forums General Discussion DS loves advanced math concepts but not practicing

Actually I'm kind of bluffing. I changed 10 to A, and 24 to B, and equated some ratios, which became a quadratic, and solving that (and dismissing the "-" solution) gives that the police car travels

A+sqrt{A^2+B^2}

This hints that there may be some kind of slick geometric argument that involves a right triangle with sides A, B, C=sqrt{A^2+B^2}, but I did not actually try to find one.

In general, the answer will involve a square root, but it just happens that if A=10 and B=24 then C=26, so you don't see the square root in the given specific problem. So in some sense, "solving a quadratic" is necessary.

I wonder if it was a multiple choice question, in which case one could just check which option works (which is still not totally trivial).

I think Pythagoras is roughly grade 6, and solving quadratics is roughly grade 8.