Question 967664
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.