SOLUTION: Okay. This is a question on my study guide for my test tommorrow and right now I am clueless on how to do this: A motorboat can go 16 miles downstreamon a river in 20 minutes. It t

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Okay. This is a question on my study guide for my test tommorrow and right now I am clueless on how to do this: A motorboat can go 16 miles downstreamon a river in 20 minutes. It t      Log On


   

Question 26919: Okay. This is a question on my study guide for my test tommorrow and right now I am clueless on how to do this: A motorboat can go 16 miles downstreamon a river in 20 minutes. It takes the same boat 30 minutes to go back upstream the same 16 miles.
a) write an equation for the motion of the boat upstream.
b) write an equation for the motion of the boat downstream.
c) find the speed of the current
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
The boat has a steady rate of speed, let's call it "r" but it's total speed is being effected by speed of the current, let's call that "c". When the boat is moving upstream, the current is fighting against the boat and is subtracting from its speed. Thus when moving upstream, the boat's motion is given by (30 min=.5 hr):
a) %28.5%29%28r-c%29=16
When it's moving downstream the boat's speed is increased by the current and it is given by (20 min=1/3 hr):
b) %281%2F3%29%28r%2Bc%29=16
To find the speed of the current, this is a good problem to use elimination. First divide 16 in your two equations by the amount of time it took to rewrite as:
r-c=16%2F.5=32 &
r%2Bc=16%2F%281%2F3%29=48
Subtract the bottom equation from the top (since we're trying to find c, if we wanted to find r first we'd add them) to get:
-2c=-16 Divide:
c=8mph