Question 636835
A river boat's speed is 5 kilometers/hour on standing water when it is charged
 and 15 kilometers an hour on standing water when it is empty.
 The boat sets sail charged up the river (against the current) to a distance
 of 81 kilometers.
 It returns (against the current) empty.
 The total sailing time there and back, including 3 hours of docking for 
unloading the cargo, is 48 hours. 
What is the speed of the current?
:
The way this reads, it is against the current up and back, but that doesn't
 make sense. Assume it returns with the current
:
Let c = rate of the current
then
(5-c) = effective speed upstream, charged
and
(15+c) = effective speed downstream, empty
:
From the information given, we know the sailing time is 45 hrs (3hrs to unload)
:
Write a time equation; time = dist/speed
:
Time up + time down = 45 hrs
{{{81/(5-c)}}} + {{{81/(15+c)}}} = 45
:
multiply by (5-c)(15+c)*
(5-c)(15+c)*{{{81/(5-c)}}} + (5-c)(15+c)*{{{81/(15+c)}}} = 45(5-c)(15+c)
:
Cancel out the denominators, results
81(15+c) + 81(5-c) = 45(75+5c-15c-c^2)
1215 + 81c + 405 - 81c = 45(75-10c-c^2)
1620 = 3375 - 450c - 45c^2
:
combine like terms on the left
45c^2 + 450c - 3375 + 1620 = 0
45c^2 + 450c - 1755 = 0
:
Simplify, divide by 45, results
c^2 + 10c - 39 = 0
Factors to 
(c+13)(c-3) = 0
the positive solution
c = 3 km/h is the current
:
:
Check the solution find the time each way
81/(5 - 3) = 40.5 hrs
81/(15 +3) =  4.5
----------------------
total time: 45 hrs; confirms our solution of current is 3 km/h
:
Did all this make sense to you here?  C