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?

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) (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

We will discount the negative value for r; speed in this problem is positive
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

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