# math

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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 -

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 -

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 -

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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