SOLUTION: A motorboat takes 5 hours to travel 150 km going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the c

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A motorboat takes 5 hours to travel 150 km going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the c      Log On


   

Question 890652: A motorboat takes 5 hours to travel 150 km going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
r, boat speed in absence of any current
c, speed of current


_______________speed________time________distance
upstream_______r-c__________5___________150
downstream_____r+c__________3___________150


SYSTEM OF EQUATIONS
---------------------------
highlight_green%28%28r-c%29%2A5=150%29
highlight_green%28%28r%2Bc%29%2A3=150%29
---------------------------

Those are two simultaneous linear equations.

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat takes 5 hours to travel 150 km going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
***
let x=rate of the boat in still water
let c=rate of current
x+c=rate of the boat downstream
x-c=rate of the boat upstream
distance/speed=travel time
..
150%2F%28x-c%29=5
150%2F%28x%2Bc%29=3
..
5x-5c=150
3x+3c=150
..
15x-15c=450 (mult. by 3)
15x+15c=750(mult. by 5)
add
30x=1200
x=40
5c=5x-150=200-150=50
c=10
rate of the boat in still water=40 km/hr
rate of current=10 km/hr