SOLUTION: 2. A boat, which moves at 11 mph in water without a current, goes 56 miles upstream and 56 back again in 11 hours. Find the speed of the current to the nearest tenth.

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Question 1072429: 2. A boat, which moves at 11 mph in water without a current, goes 56 miles upstream and 56 back again in 11 hours. Find the speed of the current to the nearest tenth.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A boat, which moves at 11 mph in water without a current, goes 56 miles upstream and 56 back again in 11 hours.
Find the speed of the current to the nearest tenth.
:
let c = the rate of the current
then
(11-c) = effective speed upstream
and
(11+c) = effective speed downstream
:
Write a time equation. time = dis/speed
up time + down time = 11 hrs
56%2F%28%2811-c%29%29 + 56%2F%28%2811%2Bc%29%29 = 11
multiply equation by (11-c)(11+c), cancel the denominators
56(11+c) + 56(11-c) = 11(11+c)(11-c)
distribute and FOIL
616 + 56c + 616 - 56c = 11(121 - c^2)
1232 = 1331 - 11c^2
11c^2 = 1331 - 1232
11c^2 = 99
c^2 = 99/11
c^2 = 9
c = sqrt%289%29
c = 3 mph is the rate of the current
:
;
Check this by finding the actual time each way
56/8 = 7 hrs
56/14 = 4 hrs
=============
tot time 11 hrs