SOLUTION: Ted 40 minutes to paint a wall. Burt can paint the same wall in 30 minutes. How long will it take for the two of them to do the job together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Ted 40 minutes to paint a wall. Burt can paint the same wall in 30 minutes. How long will it take for the two of them to do the job together?      Log On


   

Question 827737: Ted 40 minutes to paint a wall. Burt can paint the same wall in 30 minutes. How long will it take for the two of them to do the job together?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Set t = Ted's rate as houses per minute
b = Burt's rate as houses per minute
(t Ted's rate)/( 1 minute ) = (1 house)/( 40 minutes )
t%2F1+=+1%2F40
cross products gives us
40t = 1
divide each side by 40
t = 1/40 in terms of houses per minute
b%2F1+=+1%2F40
cross products gives us
30b = 1
divide each side by 40
b = 1/30 in terms of houses per minute
rate * time = houses
( 1/40 + 1/30 )* x = 1 where x is the amount of time
( 1/40 + 1/30 )* x = 1
using common denominator 120
( 3/120 + 4/120 ) * x = 1
( 7/120 )*x = 1
multiply each side by 120/7
x = 1*(120/7)
x = 17.14 minutes