math
posted by Lori on .
A tugboat goes upstream 120 miles in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without the current and the speed of the current.

Setup:
Let v=speed of boat
c=speed of current
Distance = speed*time
Upstream:
120=(vc)*20 ...(1)
Downstream:
120=(v+c)*10 ...(2)
Solve for v and c. 
Okay, I got:
v+6c and c=c6 for 120=(vc)*20
AND:
c=12v and v=6/5c for 120=(v+c)*10
Now what do I do? 
What you really want to do is to reduce the variables in simpler terms by dividing both sides by 20:
vc=120/20=6 ...(1a)
v+c=120/10=12...(1b)
This is a sum and difference form where the solution can be done mentally:
v=(sum+difference)/2=9
c=(sumdifference)/2=3