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

Algebra ->  Customizable Word Problem Solvers  -> Travel -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-1x%2B-72+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A2%2A-72=577.

Discriminant d=577 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+577+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+577+%29%29%2F2%5C2+=+6.25520607473216
x%5B2%5D+=+%28-%28-1%29-sqrt%28+577+%29%29%2F2%5C2+=+-5.75520607473216

Quadratic expression 2x%5E2%2B-1x%2B-72 can be factored:
2x%5E2%2B-1x%2B-72+=+2%28x-6.25520607473216%29%2A%28x--5.75520607473216%29
Again, the answer is: 6.25520607473216, -5.75520607473216. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-72+%29

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