Math question: What is the answer and how do you work this out?

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 minutesMath question: What is the answer and how do you work this out?
You can actually reason through this without much of math.





Since one person can paint this house in 4 hours, any answer taking more than 4 hours are obviously wrong. That takes D and E out of the pool of possible answers.





Since one person can paint this house in 6 hours, if the other person can paint in 6 hours, it will take half that time, which is 3 hours. That makes any answer greater than 3 hours wrong. That takes B and C out of the pool.





Now, since the other person can paint it faster than 6 hours, together, they must be able to complete the task in less than 3 hours.





That only leaves A as a valid answer.Math question: What is the answer and how do you work this out?
If it were a multiple choice test and those were the options I would use fractions to get close enough to guesstimate.





In one hour Sally paints 1/4th of the house and John paints 1/6th of the house. Using least common denominators, Sally does 3/12ths and John does 2/12ths in one hour. So in two hours they've done 10/12ths. With 2/12ths left it should take the both of them less than half an hour, so I would guess A.
Sally's rate + John's rate = rate together


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


(1 / 4)(3 / 3) + (1 / 6)(2 / 2) = 1 / x


(3 / 12) + (2 / 12) = 1 / x


5 / 12 = 1 / x


5 * x = 1 * 12


5x = 12


5x / 5 = 12 / 5


x = 2.4 hours





2.4 hours =


2 hours + 0.4 hours =


2 hours + [0.4 hours * (60 minutes / hour)] =


2 hours + 24 minutes =


2 hours and 24 minutes





ANSWER: A: 2 hours and 24 minutes
Let S = 1/4 representing the portion of a house per hour for Sally.


Let J = 1/6 representing the portion of a house per hour for John.


Let t = time in hours





Thus t x ( S + J ) = one house painted.


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


t x ( 3/12 + 2/12 ) = 1


t x 5/12 = 1


t = 12/5 hours


t = 2 hours 24 minutes
A. 2 hours and 24 minutes


You do 1/4+1/6=1/x


Then find the LCD(least common denominator) for all three, which is 24x.


Then you multiply 24x by 1/4, 1/6, and 1/x and get 6x+4x=24


Then the answer is 2.4 hours which is 2 hours and 24 minutes
ha, i asked this exact same question on here.





sally can paint 1/4 house in an hour, john can paint 1/6 house per hour.











X/4 + X/6= 1





get same denominators





3X/12 + 2X/12 = 12/12





3x+2x = 12


5x=12


x=2.4 hours, 2 hours and 24 minutes





answer: A
H = S * 4 hours


H= J * 6 hours








H = S t + J t


H = (S + J)t = (H/4 + H/6)t


(3 + 2) t = 12


t = 2 and 2/5
isnt it 5hrs as its the average of both painters times
none of them