SOLUTION: Two painters josh and Bose can paint the four walls of a room together in 6 hours whose walls are 3m high and whose floor area is 4m by 8m. Josh is a more careful painter and so

Question 967664: Two painters josh and Bose can paint the four walls of a room together in 6 hours whose walls are 3m high and whose floor area is 4m by 8m. Josh is a more careful painter and so does about a fifth less the amount of work that Bose does. If Bose works on his own on the next job, how much time will it take him if the next job is a 1200 m^2 of painting work?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
they paint 4 walls.
2 of the walls are 3 * 4 = 12 * 2 = 24 square meters of area.
2 of the walls are 3 * 8 = 24 * 2 = 48 square meters of area.

the total square feet of area painted is 72 square feet.

josh paints 4/5 of the area that bose paints.

let x equal the amount that bose paints and you get the formula:

4/5 * x + x = 72

combine like terms to get 9/5 * x = 72.

solve for x to get x = 5/9 * 72 = 40.

4/5 * x is therefore equal to 4/5 * 40 = 32.

josh paints 32 square meters in 6 hours and bose paints 40 square meters in 6 hours.

together they paint 72 square feet in 6 hours.

since rate * time = quantity of work, then:

josh formula of rate * time = quantity becomes r * 6 = 32.
solve for r to get josh rate is equal to 32/6 square meters in one hour.

bose formula of rate * time = quantity becomes r * 6 = 40.
solve for r to get bose rate is equal to 40/6 square meters in one hour.

does this makes sense?

josh r = 32/6.
rate * time = quantity
32/6 * 6 = 32 checks out ok.

bose r = 40/6.
rate * time = quantity
40/6 * 6 = 40 checks out ok.

the rates are correct.

when bose works alone, and bose has to paint 1200 square meters, the formula becomes:

40/6 * time = 1200 square meters to be painted.
solve for time to get time = 1200 * 6 / 40 = 180 hours.

bose would take 180 hours to paint 1200 square meters working at the rate of 40/6 meters per hour.

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