Question

1) Lance can paint the room in 5 hours, while Kim can paint the same room in 4 hours.

How many hours would it take for them to paint the room together?

2) Dominique can ice cupcakes twice as fast as Houston. When they work together, Dominique and Houston can ice a large order of cupcakes in 5 hours.
How many hours would it take Houston to ice them by himself?

Answer 1

In 1 hour, Lance can paint
`(1)/(5)` of the room.
In 1 hour, Kim can paint
`(1)/(4)` of the room.
In 1 hour both will paint;

`(1)/(5) + (1)/(4)`

`(4)/(20) + (5)/(20)`
=
`(9)/(20)`

Together they will take;

`(20)/(9)`
=2
`(2)/(9)`

Answer 2

1. In an hour, Lance can do 1/5 of the job and Kim can do 1/4 of the same job. Letting x be the number of hours it will take them to do the job together.
(1/5 + 1/4) x = 1
The value of x is 20/9 or approximately 2.22 hours.

2. Same as the concept above, the equation that would best describe the situation is,
(1/x + 1/2x)(5) = 1
The value of x is 7.5 hours. Since this value is the number of hours Dominique can do the job alone, Houston's time will be 15 hours.