You travel north 5 miles then south 3 mile in the same amoun

You travel north 5 miles then south 3 mile in the same amount of time. Your speed going south was 6 mph than going north. Find the speed each way and the amount of time spent going each direction.

Solution

We use the equation distance/time = speed. Rearranged is distance/speed = time.
D/S = T
We travelled north 5 miles in speed that is 6 mph more than we travelled south. So we can say:
5/(x+6)
Where x is the unknown speed.
We travelled south at x speed:
3/x
Now because we know that the time taken to travel these two distance was the same we can say these two equations equal each other:
5/(x+6) = 3/x
So we need to rearrange to get x on its own:
5x/(x+6) = 3
5x = 3x+18
2x = 18
x = 9
So the speed going north was 15 mph, speed going south was 9mph. Time going north was 5 miles divided by 15 mph = 1/3 hour or 20 minutes which is the same time going south.