SOLUTION: A man takes 1 hour to row 2km upstream and return. The river has a current of 2kph. Find the speed of the man in still water?

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Question 158338: A man takes 1 hour to row 2km upstream and return. The river has a current of 2kph. Find the speed of the man in still water?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let r=rate (speed) of the man in still water
Time to travel upstream =2/(r-2) (upstream we need to subtract the speed of the current)
Time to travel downstream=2/(r+2) (downstream we add the speed of the current)
Now we are told that the above two times add up to 1 hour, so:
2/(r-2) + 2/r+2)=1 multiply each term by (r-2)(r+2)
2(r+2)+2(r-2)=(r-2)(r+2) get rid of parens
2r+4 +2r-4=r^2-4 or
4r=r^2-4 subtract 4r from each side
r^2-4r-4=0 quadratic in standard form; solve using the quadratic formula
r+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
r+=+%284%2B-+sqrt%28%28-4%29%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%29+
r+=+%284%2B-+sqrt%2816%2B16+%29%29%2F%282%29+
r+=+%284%2B-+sqrt%2832+%29%29%2F%282%29+
r+=+%284%2B-+5.66%29%2F%282%29+
We will discount the negative value for r; speed in this problem is positive
r=%284%2B5.66%29%2F2=9.66%2F2=4.83 kph---speed of man in still water
2/(4.83-2) +2/(4.83+2)=1
2/2.83 +2/6.83=1
0.707+0.293=1
1=1
Hope this helps---ptaylor