If Bob can build a brick wall in 8 hours and Butch can build the same wall in 5 hours...?

Bob's rate = 1 wall / 8 hours

Butch's rate = 1 wall / 5 hours

(Bob + Butch)'s rate = 1/8 + 1/5 wall/hours = (5+8)/(5*8) wall/hour = 13/40 wall/hour

number of walls built = time * (rate of building walls)

we want 1 wall and we calculated the rate, so solve for time:

time = 1 wall / (13/40 wall/hr) = 40/13 hour = 3.08 hour

gatorbait's answer below can't be right (6.5 hr). why not just let Bob sleep and have Butch do it in 5 hour!! if it takes longer, than Bob isn't building walls, but tearing them down. always do a "sanity check" on your answer.

Bob and butch build 2 walls in 8 + 5 hours = 2 walls in 13 hours.

So...working together they can build 1 wall in 13/2 = 6 1/2 hours

Bob's rate is 1/8 and Butch's is 1/5. So I think you can add the rates to get the total as:

(1/8) + (1/5) = 1/X (that is one wall in X hours)

solve for X to get the number of hours:

(13/40) = 1/X

X = 40/13 hours. you might want to check my work.

3 hours

I think, if they were work together, they will need around 3.5 to 4 hours to finish what they started. But, it all matter of cooperation and tolerence between them.