Question 291097: Juniors boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current?
Answer by Grinnell(63)   (Show Source):
You can put this solution on YOUR website! As in all Speed (Rate) Distance problems we start out with the formula rate Times time =distance--
Rate x Time = Distance
the speed in still water is 15mph
BUT we are given a current which will add to the speed in still water as the boat goes DOWNSTREAM.
Let current be x (keeping our variable simple, ok?)
The current takes away from the speed in still water by the same variable x.
So, (15+x) TIMES time =12
(15-x) TIMES time =9
Since we are given that the time is the same--T
we can divide by 15+x (in the first equation) and 15-x (in the second equation) and get 12/15+x =9/15-x
STOP. Understand what I just did. Both sides of the above equations equal T, I substituted.
Now we solve for x!
We multiply thru by (15+x) and (15-x)
We get 180-12x=135+9x
-21x=-45
x=2 and 1/7mph. Let's check it.
2 and 1/7=roughly 2.14
Let's put it in -- 17.14---our time should come out to be equal, or the SAME time!
12/17.14=.700
9/12.86=.699 This is close enough. The speed is then 2.14 miles per hour. Remember this is 45/21. I rounded off.
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