Simple distance problem

A man covers a distance on his scooter. If he had traveled 3 kmph faster he would have taken 40 minutes less. If he had traveled 2 kmph slower he would have taken 40 minutes more. Find the distance he traveled?

Internet solution:

Let r be the unknown rate and t the unknown time;

r*t = (r+3)(t-2/3)

r*t = (r-2)(t+2/3)

I then have to find r and t.

How do I find r and t?

I don't understand what I am actually solving?

If he traveled the same distance why can't I just, solve for a=b. But then I won't be able to solve the simultaneous equation?

I am not expecting a total solution just want an idea of what to solve......

r is the speed that he actually travelled, and t is the time actually taken. r*t gives us the distance travelled.

The units being used are km and hours.

What the two simultaneous equations are saying is that if you vary the speed and time in a certain way then the distance r*t stays the same.

Your eventual goal is to find the distance which is r*t. One way of finding this is to calculate r and t then multiply them.

This brings us to the simultaneous equations. They're not in the usual form that simultaneous equations come in but they're still manageable. One way you could start off is to multiply out all the brackets and see if there are any terms you can cancel. This should put it into the form of two simultaneous linear equations which should be easier to solve.