SOLUTION: A boat moves 9 kilometers upstream in the same amount of time it moves 19 kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in s

Algebra ->  Human-and-algebraic-language -> SOLUTION: A boat moves 9 kilometers upstream in the same amount of time it moves 19 kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in s      Log On


   

Question 159403: A boat moves 9 kilometers upstream in the same amount of time it moves 19 kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still water.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
boat moves 9 kilometers upstream in the same amount of time it moves 19 kilometers downstream. If the rate of the current is 9 kilometers per hour, find the rate of the boat in still water.
:
Let x = speed in still water
then
(x+9) = speed downstream
and
(x-9) = speed upstream
:
Times of the two trips are equal; write a time equation from this fact:
Time = dist%2Fspeed
:
Downstream time = Upstream time
19%2F%28%28x%2B9%29%29 = 9%2F%28%28x-9%29%29
Cross multiply:
19(x-9) = 9(x+9)
:
19x - 171 = 9x + 81
:
19x - 9x = 81 + 171
:
10x = 252
x = 252%2F10
x = 25.2 km in still water
:
:
Check solution by confirming the times are equal:
19/34.2 = .56 hrs
9/16.2 = .56 hrs