SOLUTION: In coloradoCreek, Darrell can row 24 km down stream in 6 hours or he can row 18 km upstream in the same amount of time. Find the rate he rows in still water and the rate of the cur

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Question 110682: In coloradoCreek, Darrell can row 24 km down stream in 6 hours or he can row 18 km upstream in the same amount of time. Find the rate he rows in still water and the rate of the current.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let R = Darrell's rowing speed in still waters and C = The current speed.

From the the problem description, you can write:
1) d%5B1%5D+=+r%5B1%5Dt%5B1%5D For the downstream trip.
2) d%5B2%5D+=+r%5B2%5Dt%5B2%5D For the upstream trip.
1) 24+=+r%5B1%5D%286%29
r%5B1%5D+=+4
2) 18+=+r%5B2%5D%286%29
r%5B2%5D+=+3
The downstream trip rate can be thought of as Darrells's rowing speed plus the current speed, or:
r%5B1%5D+=+R%2BC or:
4+=+R%2BC
The upstream trip rate can be thought of as Darrell's rowing speed minus the current speed, or:
r%5B2%5D+=+R-C or:
3+=+R-C
So you can add these two equations to find the value of R, Darrell's rowing speed in still water:
4+=+R%2BC
3+=+R-C
-------------
2R+=+7
R+=+3.5
Darrell's rowing speed in still water is 3.5 km/hr.
The current speed is:
C+=+R-3
C+=+3.5-3
C+=+0.5km/hr