SOLUTION: A stream flows at a rate of 4mph. A boat travels 70 miles downstream and returns in a total time of 6hr. What is the speed of the boat in still water?

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Question 760966: A stream flows at a rate of 4mph. A boat travels 70 miles downstream and returns in a total time of 6hr. What is the speed of the boat in still water?

Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
A stream flows at a rate of 4mph. A boat travels 70 miles downstream and returns in a total time of 6hr. What is the speed of the boat in still water?
Let x be the speed of boat in still water.
Then, the speed of the boat downstream = x%2B4 (since it flows with the current) and speed while returning upstream = x-4
Time taken to travel 70 km downstream = 70%2F%28x%2B4%29
Time taken to travel 70 km upstream = 70%2F%28x-4%29
Total time = 70%2F%28x%2B4%29+%2B+70%2F%28x-4%29+=+6
70%2A%28x-4%29+%2B+70%2A%28x%2B4%29+=+6%2A%28x%2B4%29%2A%28x-4%29
140%2Ax+=+6%28x%5E2+-+16%29
6%2Ax%5E2+-+140%2Ax+-+96+=+0 We can solve this using the standard formula for solving quadratic equations.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B-140x%2B-96+=+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=%28-140%29%5E2-4%2A6%2A-96=21904.

Discriminant d=21904 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--140%2B-sqrt%28+21904+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-140%29%2Bsqrt%28+21904+%29%29%2F2%5C6+=+24
x%5B2%5D+=+%28-%28-140%29-sqrt%28+21904+%29%29%2F2%5C6+=+-0.666666666666667

Quadratic expression 6x%5E2%2B-140x%2B-96 can be factored:
6x%5E2%2B-140x%2B-96+=+6%28x-24%29%2A%28x--0.666666666666667%29
Again, the answer is: 24, -0.666666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-140%2Ax%2B-96+%29




The roots of the equation are x = 24, x = -0.67
Since x cannot be negative, the speed of the boat in still water = 24 mph