SOLUTION: A boat takes 3 hours to go 9 miles upstream. It can go 18 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water.​ (Hint: Bec

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Question 1020892: A boat takes 3 hours to go 9 miles upstream. It can go 18 miles downstream in the same time. Find the 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 sum 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.)
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Implied variable assignings, 
                 rate             time            distance

UP              r-c                3                 9

DOWN            r+c                3                18

Form the system according to RT=D,
system%28%28r-c%29%2A3=9%2C%28r%2Bc%29%2A3=18%29
and solve the system.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A boat takes 3 hours to go 9 miles upstream. It can go 18 miles downstream in the same time. Find the 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 sum 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.)
let x=rate of boat in still water
let c=rate of current
(x+c)=rate of boat downsream
(x-c)=rate of boat upsream
travel time*rate=distance
3(x-c)=9 (upstream)
3(x+c)=18 (downstream)
3x-3c=9
3x+3c=18
add:
6x=27
x=4.5
3c=18-3x=18-13.5=4.5
c=1.5
rate of boat in still water=4.5 mph
rate of current=1.5 mph