As a punishment for something naughty that we did, my little brother and I have to whitewash both sides of a fence. We start at the same time, and we each work at a constant rate.

If we each whitewash one side, I'll finish in $2$ hours and my brother will finish in $3$ hours. But I'm a nice kid, so after I finish my side, I go around to the other side and help my brother finish his side. From the time I start helping him, how many minutes does it take us to finish the job?
(Just ANSWER)

Question

As a punishment for something naughty that we did, my little brother and I have to whitewash both sides of a fence. We start at the same time, and we each work at a constant rate.

If we each whitewash one side, I'll finish in $2$ hours and my brother will finish in $3$ hours. But I'm a nice kid, so after I finish my side, I go around to the other side and help my brother finish his side. From the time I start helping him, how many minutes does it take us to finish the job?
(Just ANSWER)

snuggielad · Answer

We can't just answer the question. It's against the Code of Conduct that we all agree to upon signing up. It is punishable by banning.

However, I can assist you but I need you to work with me.

Where do you think you should start?

anonymous · Answer

Ok assigning variables?

snuggielad · Answer

That should work, however the dollar signs are throwing me off. Are we talking about a length is time, or price per hour?

anonymous · Answer

length of time

snuggielad · Answer

Alright, where should the variables go?

anonymous · Answer

you would use 2x and 3x

anonymous · Answer

Then...........................

anonymous · Answer

so 2x + 3x = x (I'm pretty sure)

anonymous · Answer

that doesn't make sense srry

phi · Answer

I use the idea of 
rate * time = 1 job

and rate is in terms of "jobs per hour"  and time is in hours

phi · Answer

In this problem I would call the job "paint 1 side"
and the rates are
$$ my\ rate = \frac{1 \ side}{2 \ hours} \ brothers \ rate =   \frac{1 \ side}{3 \ hours} $$

after I finish my side.  when does that happen?  You should expect 2 hours, but using the equation
$$ rate \cdot time = 1 \ side\ \frac{1}{2}\cdot  t = 1 \ t= 2 \ hours$$
just to show how to do it that way.
Meanwhile, the other guy did some work. How much did he do in 2 hours?
Using his rate we get
$$ \frac{1}{3} \cdot 2 = \frac{2}{3} \ side$$
He painted ⅔ of a side and there is ⅓ of a side go go.

phi · Answer

working together, they have to finish ⅓ of a side
$$ \frac{1}{2} t + \frac{1}{3} t = \frac{1}{3} $$
Can you finish to find t in hours?
From the time I start helping him, how many minutes does it take us to finish the job?
then change that into minutes