Question

Camille and Lawrence can each mop the floor and vacuum the carpets at their house in two hours. Gaston needs three hours do the same job by himself. If Camille Lawrence and Gaston work together how long will it take them to clean the house

Answer 1

It will take them 3/4 of an hour together.

Camille can mop and vacuum 1/2 of the house per hour.
Lawrence can mop and vacuum 1/2 of the house per hour.
Gaston can mop and vacuum 1/3 of the house per hour.

Working at this rate for x amount of time, they can all three complete 100% of the job:

1/2x+1/2x+1/3x=1

Combining like terms,
1 1/3x = 1
3/3x + 1/3x = 1
4/3x = 1

Divide both sides by 4/3:
4/3x÷4/3 = 1÷4/3
x = 1/1÷4/3
x = 1/1×3/4
x = 3/4