A boat takes 6 hours to go 30 miles upstream it can go 72 mi

A boat takes 6 hours to go 30 miles upstream. it can go 72 miles downstream in the same time. find rate of the current and the rate of the boat in still water. (hint: because the current pushes the boat when it is going downstream, the rate of the boat downstream is the same of the rate of the boat and the rate of the current. the current slows down the boat when it is going upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the current)

Solution

First of all, rate times time equals distance, or rt=d.
Next, let\'s call the rate of the boat in still water, r.
Then, let\'s call the rate of the current, c.
Going upstream we have
6(r - c) = 30 OR r - c = 5
Goind downstream we have
6(r + c) = 72 OR r + c = 12
We add the second set of equations and get
2r = 17
r = 8.5 mph
c is then 3.5 mph.