SOLUTION: Kurt rows 72 km upstream and 72km back in a total of 7hrs. The speed of the river is 3km/h. Find kurt's speed in still water.

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Question 136098: Kurt rows 72 km upstream and 72km back in a total of 7hrs. The speed of the river is 3km/h. Find kurt's speed in still water.
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
Let s=Kurt's speed in still water.
d=st
s-3=speed upstream
s+3=speed downstream
t=time upstream
7-t=time downstream
.
A) t(s-3)=72 upstream
B)
-(t-7)(s+3)=72 Downstream
-ts+7s-3t+21=72
.
A) t=72/(s-3)
B)
-72/(s-3) * s + 7s - 3*72/(s-3)=72-21 replace t with 72/(s-3)
-72s/(s-3) + 7s - 216/(s-3)=51
-72s+7s(s-3)-216=51(s-3) multiply each side by s-3 to eliminate fractions.
-72s+7s^2-21s-216=51s-153
-72s+7s^2-21s-216-51s+153=0
7s^2-144s-63=0
s=21 kph (see below)
.
Check:
t=72/21-3=72/18=4h upstream
7-4=3h downstream
18*4=72
24*3=72
.
Ed
.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=22500 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 21, -0.428571428571429. Here's your graph: