SOLUTION: In still water, Mo and Sally can paddle a canoe at 12 mph. It takes them a total of 6 hours to paddle 32 miles up a river and then return the same distance to their starting point.

Question 940709: In still water, Mo and Sally can paddle a canoe at 12 mph. It takes them a total of 6 hours to paddle 32 miles up a river and then return the same distance to their starting point. What is the rate of the current?

Found 2 solutions by josmiceli, macston:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
mi/hr is their speed in still water
Let = the speed of the current in mi/hr
= their speed in mi/hr going downriver
= their speed in mi/hr going upriver
Let = their time in hours to go upriver
= their time in hours to go downriver
------------------------------------------
Equation for going upriver:
(1)
Equation for going downriver:
(2)
----------------------------
(1)
(1)
(1)
and
(2)
(2)
---------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
(2)
(2)
Use the quadratic formula

hrs ( I picked the right square root because
the trip upriver should take longer than downriver )

hrs
-------------------
(1)
(1)
(1)
(1)
The rate of the current is 4 mi/hr
------------------------------
check:
(2)
(2)
(2)
(2)
OK

Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
First they went 32miles against the current given by:
where c is the speed of the current and 12mph is their normal speed
Then downstream given by:

And for the total trip
Multiply both sides by 12mph-C

Multiply both sides by (12mph+C)

Divide both sides by 6

subtract 128 from both sides
Add to both sides
so c = plus/minus 4 So the current is 4 MPH
CHECK:
upstream + downstream= 6 hours
upstream=
downstream=

2Hrs + 4hrs= 6hrs

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