A simple math question...?

Let
t = amount of time to paint house together

t/4 + t/6 = 1

Multiply thru by 12 to clear the denominators.

3t + 2t = 12
5t = 12
t = 12/5 hours = 2.4 hours = 2 hours, 24 minutes

sally's work rate = 1/4 house per hour
john's work rate = 1/6 house per hour

total work rate = 1/4 + 1/6 house per hour
... = 3/12 + 2/12 house per hour
... = 5/12 house per hour

work rate = number of houses / number of hours
number of hours = number of houses / work rate
number of houses = 1
number of hours = 1 / work rate
... = 12/5 hours
... = 2.4 hours


@ Dave: so you believe that sally and john working together would take longer to paint the house than sally working by herself? well, that may be true, but if john would stop staring at sally's butt, he might be helping rather than getting in the way....

Sally points one house every four hours. Thus, she paints 1/4 house per hour.

Similarly, John paints 1/6 house per hour.

Together, they paint 1/4 + 1/6 = 5/12 house per hour.

Think of this as (5 houses)/(12 hours)

Thus, it would take them 12 hours to paint 5 houses.

The answer is that together, they paint one house in 12/5 =2.4
hours.

sally=1 house/4 hours
that is 1/4 house/hour
John=1 house/6 hours
that is 1/6 house/hour
together they pait 1/4+1/6 house/hour
that is 5/12 house/ hour
5 houses/12 hours
that is 1 house/2.4 hours
1 house/2 hr 24 min

Let area to be painted be X m ²
Sally: rate of work = X / 4 m ² / h
John: rate of work = X / 6 m ² / h

Combined rate = X / 4 + X / 6 m ² / h = 5X / 12 m ² / h
Combined rate = 5X / 12 m ² / h

Time = Area / rate

Time = X / (5X / 12) h

Time = 12 / 5 h = 2 h 24 min

Let
t = amount of time to paint house together

t/4 + t/6 = 1

Multiply thru by 12 to clear the denominators.

3t + 2t = 12
5t = 12
t = 12/5 hours = 2.4 hours = 2 hours, 24 minutes

Sal can paint 1/4 house per hour while slowpoke John can paint only1/6 house per hour.

Together they can paint 1/4 + 1/6 = 10/24 = 5/12 house per hour.

Time to paint the house is 12/5 hours = 2 2/5 hours.

Sally use 4 hours to paint a house.
John use 6 hours to paint a house.

Sally use 1 hour to paint 1/4 of the house.
John uses 1 hour to paint 1/6 of the house.

1/4 + 1/6 = 5/12 ( after 1h they paint)

12/5 = 2.4h = 2h 24min (the answer)

Sally = 4/1 hours/house = 1/4 house/hour
John = 6/1 hours/house = 1/6 house/hour

Sally + John
= (1/4 + 1/6) house/hour
= (3/12 + 2/6) house/hour
= 5/12 house/hour
= 12/5 hours/house (2.4 hours per house)

Time together
= 1 divided by (1/4 + 1/6)
= 1 divided by (3/12 + 2/12)
= 1 divided by (5/12)
= 1(12/5) = 12/5 = 2 2/5 days = 2.4 days