Larry takes 1 1/2 times as long to go 72 miles upstream as he takes to go 72 miles downstream. If the speed of the boat in still water is 30mph, what is the speed of the current?

The answer is provided for this one as 6mph, but I don't even know where to begin in setting it up. Help?

Larry travels the same distance in both directions, right? So distance traveled upstream = distance traveled downstream = 72 miles. Since distance = rate * time, you can say that rate*time upstream is the same as rate*time downstream.

Let's call the time is takes to travel downstream t. That means that the time it takes to travel upstream is 3t/2 (i.e. 1 1/2 times as long). Meanwhile, we know that the rate of travel downstream is 30+x, where x is the speed of the current, and the rate of travel upstream is 30-x.

Now just put it all together:

r*t upstream = r*t downstream
(30-x)(3t/2) = (30+x)t

The t on both sides cancels:

(30-x)(3/2) = 30+x

45 - 3x/2 = 30 + x

15 = 5x/2

30 = 5x

6 = x

So the speed of the current, x, is 6mph.