Sally can paint a house in 4 hours and John can paint it in 6 hour,?

Question

how long will it take for both of them if they paint the same how together.

Answer 1

You can think about it this way. Sally can do 1/4 of the job in 1 hour. John can do 1/6 of the job in 1 hour. so the two of them together can do (1/4)+(1/6) = 5/12 of the job in 1 hour.
So say (5/12) x N hours = 1 (the whole job), where N is the number of hours. so N hours = 1/ (5/12)
N = (12/5)
It will take 12/5 hours or 2.4 hours for them together to finish the job or 2 hours and 24 minutes

Answer 2

If Sally can paint a whole house in 4 hours, why would it take her 5 hours if John is helping her? Remember that in the hours they are working, they are doing so at the same time! Here was my reasoning:

Sally takes 4 hrs to paint 100% of the house.
John takes 6 hrs to paint 100% of the house.

If they both agreed to paint only 50% of the house, then Sally would be done in 2 hrs and John after 3hrs. However, once Sally was done, she would likely continue and help finish John's side. That means that there is a fraction in there.

Sally works 1/3rd faster than John, so she would then help finish John's remaining portion. Since John has an hour of work left, he would be able to do one more third while Sally finished the other two thirds.

So I believe that the answer should be 2hrs 40min. But it has been over twenty years since I was out of school so I will set this question on my watch list and hope you share the correct answer with us later ;-)

Answer 3

Sally & John when painting the house, would distribute the work, equally... that is Sally paints half and the rest half is done by John. In this case, Sally will tgake 2 hours and John will take 3 hours to paint their respective portions of the house.

Now, assuming that they both begin at the same point of time, the house will be completed in 3 hours...

Answer 4

Works done by Sally in 1 hour is 1/4
Works done by John in 1 hour is 1/6
Works done by both in an hour is 1/4 + 1/6 = 3/12 + 2/12 = 5/12

Hours required to complete a job if they work together is 12/5 hours (ie 12/5 * 60 mins = 144 mins or 2 hrs 24 mins).

(Note: Hours and Work are inversly propotional)

Answer 5

Sally can paint the house in 4 hours, so with John's help, she should be able to finish the house in half that time, or a little more then half. I would say 2 hours or 2 1/2 Hours.

Answer 6

It should take them 4-5 hours, because it would take Sally 2 hours to paint half the house and John 3 hours to paint half the house.

Answer 7

Sally'4 hours + John's 6hours = 2 house painted (10hrs) This Means that if they both painted an entire house after ten hours they would have painted 2 houses. So if they both painted it would take 5 hours to paint one house, but Sally would have painted2/3 the house (4/6=2/3)
This makes sense to me, but my math is terrible! It's entirely possible (more than possible) the 2 hrs is right.

I'm editing/postscripting this. I'm sure this answer is wrong but if it is, it's comforting to know I'm not the only idiot.

Answer 8

2 hours

Answer 9

2 hours and 24 minutes

Answer 10

5 hours