Posted by **Lori** on Wednesday, August 1, 2012 at 6:32pm.

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.

- math -
**MathMate**, Wednesday, August 1, 2012 at 6:45pm
Set-up:

Let v=speed of boat

c=speed of current

Distance = speed*time

Upstream:

120=(v-c)*20 ...(1)

Downstream:

120=(v+c)*10 ...(2)

Solve for v and c.

- math -
**Lori**, Wednesday, August 1, 2012 at 7:03pm
Okay, I got:

v+6-c and c=c-6 for 120=(v-c)*20

AND:

c=12-v and v=6/5-c for 120=(v+c)*10

Now what do I do?

- math -
**MathMate**, Wednesday, August 1, 2012 at 7:13pm
What you really want to do is to reduce the variables in simpler terms by dividing both sides by 20:

v-c=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=(sum-difference)/2=3

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