Dad took his son on a trip. Dad told his son to go first 100 step before catching up.

It will be more convenient to unify this problem into steps.

First of all, it takes three steps for a father to take five steps for his son, so it takes nine steps for a father to take 15 step for his son.

In other words, the father took 9 steps and the son took 15 steps.

Second, the distance that the father takes 9 steps is equal to the distance that the son takes 17 steps. Therefore, if the father takes 9 steps, he will take more steps than the child. 17- 15=2 steps. In other words, for every nine steps a father takes, he will catch up with his son by two steps (depending on the size of his steps).

Thirdly, because he was ahead of 100 at first, and because his father only caught up with his son by two steps every nine steps (depending on the size of his son's steps), he had to take 50 nine steps, which is 450 steps. 、、

So in the end, dad has to take 450 steps.