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# Please help me to solve this?how long will it take for both of them to paint the house together?

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?

PLEASE HELP!

### 10 Answers

- PranilLv 71 decade agoFavorite Answer
Sally in 4 hours, and John in 6 hour

calculate the work done by them in 1 hour

Sally in 4 hours, in 1 hour 1/4 part of work done

John in 6 hour in 1 hour 1/6 part of work done

total work done in 1 hour = 1/4 + 1/6 LCM 12

total work done in 1 hour = 3/12 + 2/12

= 5/12

so 5/12 part of work requires 1 hour

then 1 full work requires 1 ÷ 5/12 hours

= 12/5 hours

= 2 2/5 hours

2/5 hours = 2/5 × 60 = 24 minutes

Time required for both of them = 2 hours 24 minutes.

- Brocko222Lv 41 decade ago
Sally paints 1/4 house in an hour

John paints 1/6 house in an hour

S + J paint 1/4 + 1/6 = 5/12 house in an hour

So S + J can paint a house in 12/5 hours = 2 2/5 hours = 2 hr 24 min

- Joel LLv 61 decade ago
Sally paints 1/4 house in an hour

John paints 1/6 house in an hour

S + J paint 1/4 + 1/6 = 5/12 house in an hour

So S + J can paint a house in 12/5 hours = 2 2/5 hours = 2 hr 24 min

- 1 decade ago
Sally paints the house in 4 hours, therefore she is painting 1/4 of the house per hour. John paints the house in 6 hours, therefore he is painting 1/6 of the house per hour.

In one hour they can both paint 1/4 + 1/6 of the house, common denominator of 12 -> 3/12 + 2/12 = 5/12 of the house per hour.

So it will take 12/5 of an hour to paint the whole house = 2 2/5 = 2.4 hours = 2 hours 24 minutes.

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- ?Lv 71 decade ago
Let x=number of hours it takes to do the job together

1/4 + 1/6 = 1/x

x=24/10=2.4 hrs

- 1 decade ago
let x be the number of hours that it takes for them to paint the house together.

x/4 + x/6 = 1

find the common denominator, and this should become a regular equation that solves for x.

The answer I got is 12/5 hours, or 2.4 hours.

- Anonymous1 decade ago
Is the painting to be done with a single brush one by one, or both persons paint on the same spot at once together?

- Jun AgrudaLv 71 decade ago
x/4 + x/6 = 1

3x + 2x = 12

5x = 12

x = 12/5

Answer: 12/5 hrs or 2.4 hrs or (2 hrs, 24 min)

- koersLv 44 years ago
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- Anonymous1 decade ago
It will take 2 hrs and 24 minutes.

If you want to know how I reached the answer, just ask me please.