According to the meaning of the question, suppose that after x hours, the two ships are the closest. The nearest distance is y kilometers.

Then from Pythagorean theorem

y^2=( 15x)^2 +( 125-20x)^2

y^2=625(x^2 -8x+25)

Accord to that property of quadratic function, when x=4,

Y 2 has a minimum value f(4)=9x625=5625.

So the minimum value of y is 75.

That is, after driving for four hours, the distance between the two ships is the shortest, which is 75 kilometers.