SOLUTION: A motorboat travels 120km upstream and then 120km downstream in a total of seven hours. If the speed of the river's current is 5km/h then what is the speed of the motorboat in stil

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A motorboat travels 120km upstream and then 120km downstream in a total of seven hours. If the speed of the river's current is 5km/h then what is the speed of the motorboat in stil      Log On


   

Question 128437: A motorboat travels 120km upstream and then 120km downstream in a total of seven hours. If the speed of the river's current is 5km/h then what is the speed of the motorboat in still water?????
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat travels 120km upstream and then 120km downstream in a total of seven hours. If the speed of the river's current is 5km/h then what is the speed of the motorboat in still water.
:
Let s = boat speed in still water
then
(s+5) = boat speed downstream
and
(s-5) = boat speed up-stream
:
Write a time equation: Time = distance%2Fspeed
:
Time up + time down = 7 hrs
120%2F%28%28s-5%29%29 + 120%2F%28%28s%2B5%29%29 = 7
:
Multiply equation by the common denominator: (s+5)(s-5), resulting in:
120(s+5) + 120(s-5) = 7(s-5)(s+5)
:
multiply what's inside the brackets
120s + 600 + 120s - 600 = 7(s^2 - 25)
:
240s = 7s^2 - 175
:
0 = 7s^2 - 240s - 175; a quadratic equation
:
This will factor to:
(7s + 5 )(s - 35) = 0
:
Positive solution:
s = +35 km/hr is boat speed in still water
:
:
Check solution using the time equation:
120%2F40 + 120%2F30 =
3 + 4 = 7 hrs