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?

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) (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 = (since it flows with the current) and speed while returning upstream =
Time taken to travel 70 km downstream =
Time taken to travel 70 km upstream =
Total time =

We can solve this using the standard formula for solving quadratic equations.

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=21904 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 24, -0.666666666666667. Here's your graph:

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