SOLUTION: If Mary can paint a house in 4 hours and it takes John 6 hours to paint the same house, how long would it take them if they worked together? The answer is 2 hours and 44 minutes.

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Question 490937: If Mary can paint a house in 4 hours and it takes John 6 hours to paint the same house, how long would it take them if they worked together? The answer is 2 hours and 44 minutes. I just cannot get there...HELP!!
Found 2 solutions by Earlsdon, Theo:
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Find the hourly rate of each painter.
If Mary can paint the house in 4 hours, then she can paint of the house in 1 hour.
If John can paint the house in 6 hours, then he can paint of the house in 1 hour.
So working together, they can paint of the house in 1 hour, which means that they can paint the entire house in hours.
hours. or hours and minutes.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
rate * time = units
the unit is equal to 1 (the house).
mary can paint the house in 4 hours.
for mary, the equation becomes:
rate * 4 = 1
solve for rate to get mary's rate = 1/4
this means that mary can paint 1/4 of the house in 1 hour.

for john the equation becomes:
rate * 6 = 1
solve for rate to get john's rate = 1/6
this means that john can paint 1/6 of the house in 1 hour.

you want to know how long it takes them to paint the house together.
if they paint the house together, then their rates are additive.
the equation you get is:

(1/4 + 1/6) * time = 1
the unit is still one.
you have the rates for mary and john that you are adding together.
now you are solving for time.

you get:
(1/4 + 1/6) * time = 1
this is equivalent to:
(3/12 + 2/12) * time = 1
this is equivalent to:
(5/12) * time = 1
divide both sides of the equation by (5/12) to get:
time = 1 / (5/12)
this is equivalent to:
time = 1 * (12/5) which is equivalent to:
time = 12/5 which is equivalent to:
time = 2.4 hours.

this is NOT equivalent to 2 hours and 44 minutes.
it is equivalent to 2 hours and 24 minutes.
.4 * 60 = 24 minutes.

let's see if the answer makes sense.
mary works for 2.4 hours so she paints 1/4 * 2.4 = .6 of the house.
john works for 2.4 hours so he paints 1/6 * 2.4 = .4 of the house.
together they paint .6 + .4 = 1 of the house.
1 of the house is the whole house, so they are done and the values for the time it takes are also good.

i don't know where you got 2 hours and 44 minutes from but it is not correct for this problem.

it should be 2 hours and 24 minutes.

2 hours and 24 minutes is equal to 2 + 24/60 = 2 + .4 = 2.4 hours which is correct.

2 hours and 44 minutes is equal to 2 + 44/60 = 2 + .733333333 = 2.73333333 hours which would not be correct.

check the problem and the answer that it should be again to make sure you are dealing with the right numbers.

if the problem is as you stated and the answer is as you stated, then there's something wrong with the way the problem has been presented.