SOLUTION: A boat, whose speed in still water is 8Km per hour travels 12Km upstream and then 16Km downstream in 8 hours (so that the boat finishes 4Km further downstream from where it started

Question 482601: A boat, whose speed in still water is 8Km per hour travels 12Km upstream and then 16Km downstream in 8 hours (so that the boat finishes 4Km further downstream from where it started). What is the speed of the current?
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
12/(8-n)+16/(8+n)=8
12(8+n)+16(8-n)=8(64-n2)
96+12n+128-16n=512-8n2
8n2-4n-288=0
2n2-n-72=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=577 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.25520607473216, -5.75520607473216. Here's your graph:

n=6.25520607473216 or -5.75520607473216
Throwing out the negative answer, we get the speed of the current to be 6.25520607473216 mph..
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