SOLUTION: A boat travels 7 km upstream and 7km back. The time for the round trip is 8 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

Algebra.Com
Question 913338: A boat travels 7 km upstream and 7km back. The time for the round trip is 8 hours. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
r*t=d
7/(r-4)+7/(r+4)=8/1
Multiply thru by 1*(r-4)(r+4)
7*1(r+4)+7*1(r-4)=8(r^2-16)
7r+28+7r-28=8r^2-128
r^2-14r-128=0
r=12.2321245982865
Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics
Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert to standard form by dividing both sides by 2:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of r is -7, we know that -7=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .


The highlighted red part must be equal to -64 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (76.25).

Since the right part 76.25 is greater than zero, there are two solutions:


, or






Answer: r=12.2321245982865, -5.23212459828649.

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=1220 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 12.2321245982865, -5.23212459828649. Here's your graph:

RELATED QUESTIONS

A boat travels 7 km upstream and 7km back. The time for the round trip is 10 hours. The... (answered by mananth)
A boat travels 7 km upstream and 7km back. The time for the round trip is 4 hrs. The... (answered by stanbon)
A boat travels 10 km upstream and 10 km back. The time for the round trip is 10 hours.... (answered by mananth)
A boat travels 8 km upstream and 8 km back. The time for the round trip is 2 hrs. The... (answered by mananth)
A boat travels 4 km upstream and 4 km back. The time for the round trip is 7 hrs. The... (answered by ikleyn)
A boat travels 3 km upstream and 3 km back. The time for the round trip is 7 hrs. The... (answered by josgarithmetic)
a boat travels 1 km upstream and 1 km back. The time for the round trip is 5 hrs. the... (answered by mananth)
a boat travels 1 km upstream and 1 km back. The time for the round trip is 5 hrs. the... (answered by ikleyn,MathTherapy)
a boat travels 1 km upstream and 1 km back. the time for the round trip is 9 hrs. the... (answered by ankor@dixie-net.com)