how do you do this algebra problem on work?

Question

person A puts up wallpaper in the bedrooms of a house in 3 hrs. person B can do the same job in 4 hrs, and person C can do the same job in 12 hrs. if all three of them work together, how many minutes will it take them to put up the wallapaper?

Answer 1

note
these are easy to set up

In one hour
A wallpapers 1/3 of the house
B wallpapers 1/4 of the house, and
C wallpapers 1/12 of the house

if x = the number of hours to wallpaper one house, then

1/3 x + 1/4 x + 1/12 x = 1
multiply each term by the LCD = 12
4x + 3x + x = 12
combine like terms
8x = 12
x = 12/8 = 3/2 = 1.5 hours = 90 minutes

Answer 2

Let area to be covered = X units²
In 1 hour:-
A covers X/3
B covers X/4
C covers X/12

Total covered in 1 h by all three
= X/3 + X/4 + x/12 units²
= 4X/12 + 3X/12 + X/12 units²
= 8X/12 units²
= 2X/3 units²

Time taken when all three working:-
= X / (2X/3) = 3/2 h
= 1h 30 min

Answer 3

You're aware that it takes about 9 months to make a baby, no matter how many eager and enthusiastic mothers you put on the job?

It's impossible for three paperhangers to work together. They get in each others' way.

However, A can do 1/3 jobs per hour, B can do 1/4 jobs per hour, and C can do 1/12 job per hour. Together, they can do 8/12 jobs per hour, and if they don't get in each others' way, it will take 90 minutes to do the job.

Ask your teacher how many paperhangers it will take, each equal to C in skill, to put up the wallpaper in 0.1 seconds....

Answer 4

=(3+4+12)/3
=19/3

Answer 5

A took: 180 minutes
B took: 240 minutes
C took: 720 minutes

so the average time they take is :
(180 + 240 + 720) / 3 = 380 minutes