# Thread: I know the answer and the formula but I can not get the right answer ?

1. ## I know the answer and the formula but I can not get the right answer ?

sally can paint a house in 4 hours and john can paint the same house in 6 hourse how long does it take for them to paint the same house together. I know the answer in 2 hours and 24 mins. and I know that we use D=RT but I can not get 2 hours and 24 mins from it. Please help. thank you.

2. sally can paint a house in 4 hours - $\displaystyle \frac{1} {4}\frac{{house}} {{hour}}$

john can paint the same house in 6 hourse - $\displaystyle \frac{1} {6}\frac{{house}} {{hour}}$

together - $\displaystyle \frac{1} {{\frac{1} {6} + \frac{1} {4}}} = \frac{{12}} {{3 + 2}} = 2\frac{2} {5} = 2\quad hours\quad and\quad 24\quad \min utes$

3. ## Another way with same result

4 hours = 4* 60 = 240 minutes
6 hours = 6*60 = 360 minutes

1/240 + 1/360 = 1/t

(multiply both side by t): t/240 + t/360 = 1

(get common denominator): 3t/720 + 2t/720 = 1

5t/720 = 1

(multiply both sides by 720) 5t = 720

(divide both sides by 5) t = 720/5

t = 144 minutes

(convert to hours):
t = 144/60 = 2 hours + (144 – 120 minutes) = 2 hours 24 minutes

4. simplest way is : let x= time . Person one is 1 house/4 hours and two is 1/6. so 1/4*x+1/6*x=1. that is x(10/24)=1 then that is 12/5 hours =x. convert that is 2 hours and 24 min.