# If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour...?

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?

A. 2 hours and 24 minutes

B. 3 hours and 12 minutes

C. 3 hours and 44 minutes

D. 4 hours and 10 minutes

E. 4 hours and 33 minutes

I cheated for the answer & looked, but I want to know how they got the answer.

Relevance

One way is to see what fraction they can do in one hour. If together it takes x hours, Sally can do 1/4 of the job in 1 hour, John can do 1/6, and together they can do 1/x.

So 1/4 + 1/6 = 1/x

3/12 + 2/12 = 1/x

5/12 = 1/x

cross multiply: 5x = 12

divide by 5

x = 12/5 hours = 2 2/5 hours = 2 hr 24 min

This is a trick question. You don't give all the Information!

What you don't know is that Sally and John are on the edge of divorce. The bills, the kids, other marital frustrations were driving them to dispair.

Their bleak future had forced them to put their home up for sale, before it was forclosed. They did all they could to bring the value of the house up. One way they could do this, they decided, was to paint it.

As they painted the house, Sally caught John asleep under the back yard tree when he was suppose to be edging the windows in paint (this is why it took him 6 hours. 2 hours for the nap)

She was so furious, she snatched the paint brush out of his hand, and rammed it down his throat.

Unable to dislodge the item, He clawed in the grass in painic. His pained face asked 'Why? oh lord, why?"

He passes out in a couple of minutes.

Brain death occurs shortly after.

20 years later, Sally is let out on parole with good behavior.

Her children had grown without knowing her, and she has a shambles of a life to put back together.

Taking whatever employment a con can get, she finds herself in front of her old home, as the current owners are trying to fix it up for sale.

For a pittance, she accepts the task of helping paint the old house- finally finishing the job she started with John 20 years ago.

so.

20 years is your answer. It takes 20 years to paint it together, start to finish.