Question 138079
The speed of a boat in still water is 10km/h. The boat travels 12km upstream and 28km downstream in a total time of 4 hours. What is the speed of the stream? 
:
Let x = speed of the current:
then
(10-x) = speed upstream
and
(10-x) = speed downstream
;
Write a time equation: Time = Dist/speed
:
Upstream time + downstream time = 4 hrs
{{{12/((10-x))}}} + {{{28/((10+x))}}} = 4
:
Multiply equation by (10-x)(10+x), get rid of the denominator, you have:
12(10+x) + 28(10-x) = 4(10-x)(10+x)
:
120 + 12x + 280 - 28x = 4(100 - x^2)
:
-16x + 400 = 400 - 4x^2
:
+4x^2 - 16x + 400 - 400 = 0
:
4x^2 - 16x = 0
:
4x(x - 4) = 0
:
x = +4 km/h is the speed of the current
:
:
Check solution by finding the times (Speed up = 6 km/h; Speed down = 14 km/h):
{{{12/6}}} + {{{28/14}}} = 4 hrs