SOLUTION: A motorboat travels 147km in 3 hours going upstream and 546km in 6 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A motorboat travels 147km in 3 hours going upstream and 546km in 6 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?       Log On


   

Question 176000: A motorboat travels 147km in 3 hours going upstream and 546km in 6 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A motorboat travels 147km in 3 hours going upstream and 546km in 6 hours going downstream. What is the speed of the boat in still water, and what is the speed of the current?
:
Let x = boat speed in still water
Let y = speed of the current
:
Write two distance equations, one for upstream and one for downstream
dist = time * speed
3x - 3y = 147
and
6x + 6y = 546
simplify, divide equation by 2
3x + 3y = 273
:
Add these two equations
3x - 3y = 147
3x + 3y = 273
-----------------addition eliminates y, find x
6x = 420
x = 420%2F6
x = 70 km/hr in still water
:
Find the current using the upstream equation
3(70) - 3y = 147
210 - 3y = 147
-3y = 147 + 210
-3y = -63
y = %28-63%29%2F%28-3%29
y = +21 km/hr is the current
:
:
Check solution in the down stream equation
6(70 + 21) =
6 * 91 = 546, confirms our solutions