How do you work this problem?

Question

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

2 hours and 24 minutes
3 hours and 12 minutes
3 hours and 44 minutes
4 hours and 10 minutes
4 hours and 33 minutes

Answer 1

Sally = 1/4 & John = 1/6

1/4 + 1/6 = 1/x

First: eliminate fractions - multiply the greatest common denominator with each term which, is 4*6*x = 24x

(24x)(1/4)+(24x)(1/6) = (24x)(1/x)

Sec: cross cancel "like" terms & combine the rest.

(24x)(1/4)+(24x)(1/6) = (24)(1)
24x/4 + 24x/6 = 24
6x + 4x = 24
10x = 24

Third: divide both sides by 10 (when you move a term to the opposite side, always use the opposite sign).

10x/10 = 24/10
x = 24/10
x = 12/5 or, 2.40

2 hours and 24 minutes

Answer 2

Sally can paint 1/4 of the house in an hour, and John can paint 1/6. Working together, they paint (1/4 + 1/6) of the house each hour. So in t hours, they'll paint the whole thing:

t(1/4 + 1/6) = 1
3t + 2t = 12
5t = 12
t = 2.4 hrs. = 2 hrs 24 min.

Answer 3

2 hours and 24 minutes
Let us assume that they can complete the work in x hours
Hence
x/4 +x/6=1
=>3x+2x=12 [multiplying all terms by 12]
=>5x=12
x=12/5 hrs=2hrs 24 min

Answer 4

it's (6*4)/ (6+4)= 24/10= 2.4 hours = 2 hours 24 minutes

Answer 5

1/4 + 1/6 = 1/x

Mult by 12x

3x + 2x = 12

5x = 12

x = 2 2/5 hr = 2 hr 24 min.