How do you do the math word problem?

Question

It it takes 26 hours for Maria to paint a house, and it takes 22 hours for Patty to paint the house, how long will it take them working together? round to the nearest minute.

Answer 1

This problem has a unique set-up. You use the time each will take by themselves in the denominator of a fraction that represents the part of the whole task that each will do. (Huh? you ask.)

For example: since it'd take Maria 26 hours to paint the whole house, in 13 hours she'd paint 13/26 = 1/2 the house (or 50%).

Similarly: in 13 hours, Patty would paint 13/22 = 59.09% of the house.

So, if you add up both these fractions, in 13 hours, both together would paint 109.09%. Obviously, they'd stop before then.

So let's let:
t = time that both girls paint the house
The part that Maria will paint is t/26
The part that Patty will paint is t/22
Together, they will paint the whole house, 100%, or 1.

t/26 + t/22 = 1 (Maria's work in t hours plus Patty's work in t hours will be 100% [1] of the whole house)
Now solve for t:
t/26 + t/22 = 1
22t + 26t = 572 <== multiply both sides by 572 (22*26)
48t = 572
t=11 11/12 hours
11/12 of an hours is 55 minutes exactly.
So, t=11 hours, 55 minutes (11:55).

Answer 2

Find the rate of each per hour. Maria does 1/26 of the job per hour to paint a house and Patty does 1/22 of the job per hour. 1 signifies a completed job so to find how long maria alone would take set x/26 = 1, meaning x hours times her rate of 1/26 equals a whole job. X = 26 hours. The same goes for Patty. Now add them together. x/26 + x/22 = 1, meaning Maria plus Patty equals a whole job in x hours. Find a common denomenator, 572 and add Patty and Maria together to get 48x/572 = 1. Now cross multiply to get x= 11.916 which rounds to 12 (minutes) for Patty and Maria to paint the house together.

Answer 3

If it takes 26 hours for Maria to paint a house and 22 hours for Patty to paint a house this means that respectively maria paints 1 house every 26 hours or 1 house/26 hours and simularly Patty paints 1 house/22 hours. So you have (1 house/26 hours + 1 house / 22 hours) x (Y hours) = 1 house.... simplify the words you have Y/26 + Y/22 = 1.... solving for Y yields 11.92 hours, or roughly 11 hours and 55 minutes. I hope this makes sense.

Answer 4

The trick to this kind of problem is: Instead of looking at how many hours it takes Maria to paint a house, flip it around and look at how many houses Maria can paint in an hour. (Actually, that will be only a fraction of one house. Specificially, 1/26 of a house.)

Do the same thing for Patty.

Now you can tell how much of a house they can finish in one hour if they work together. (Hint: it's 1/26 of a house plus 1/22 of a house.)

From that, you should be able to figure out how many hours it will take them to finish a whole house. For example, if they can finish 1/3 of a house in an hour, it'll take them 3 hours to do the whole house. Or if they can finish 1/4 of a house in an hour, it'll take them 4 hours to finish the whole house. You do the math.

Answer 5

Break it down to each hour:

Maria does 1/26 of the house in one hour, or .038462.
Patty does 1/22 of the house in one hour, or .045455.

Each hour together, they do .083916 of the total job (or 1/26 + 1/22). So, divide 1 (for the total job) by the amount they do each hour (.083916) to find out how many hours it takes: 11.91667. That comes out to 11 hours and 55 minutes.

Answer 6

Let the time working togeter be t.
(1/26 + 1/24)t = 1
t = 26*24/50 = 12.48 hours

Answer 7

youd find the average of the two, right?
24 hours