SOLUTION: In 6 hours two men can row 16 miles downstream on a river and back. their rate upstream is twice the rate of the current. find the rate at which they row in still water and the rat

Question 952783: In 6 hours two men can row 16 miles downstream on a river and back. their rate upstream is twice the rate of the current. find the rate at which they row in still water and the rate of the current. I hope you could help me. this is in a chapter in our book concerning word problems on simultaneous systems involving quadratic.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
In 6 hours two men can row 16 miles downstream on a river and back. their rate upstream is twice the rate of the current. find the rate at which they row in still water and the rate of the current.
----------------
c = current speed
b = boat's speed wrt the water
r = rate wrt Earth
----
Upstream, r = b - c = 2c --> b = 3c
downstream, r = b + c = 4c
================
Avg of the round trip is 2*3c*4c/(3c + 4c) = 24c/7 mi/hr
RT avg = 2*16/6 = 16/3 mi/hr
----
24c/7 = 16/3
72c = 112
c = 14/9 mi/hr
b = 14/3 mi/hr
=================
Check:
d'stream: r = 56/9 mi/hr --> t = d/r = 16/(56/9) = 18/7 hours
u'stream: r = 14/3 mi/hr --> t = d/r = 16/(14/3) = 24/7 hours
18/7 + 24/7 = 6 hours
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