Question

Mark can clean his father's office in 30 minutes. His younger sister Lynn can clean the office in 40 minutes. How long will it take the two of them together to clean the office?

Answer 1

Mark's rate:
( 1 office cleaned ) / ( 30 min ) = 1/30
Lynn's rate:
( 1 office cleaned ) / ( 40 min ) = 1/40
Let (a) = the time in minutes for them 
to clean the office working together
$\frac{1}{30}$ + $\frac{1}{40}$ = $\frac{1}{a}$
Multiply both sides by 120a
4a + 3a = 120 
7a = 120 
a = 17.143
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CHECK YOUR ANSWER:
$\frac{1}{30}$ + $\frac{1}{40}$ = $\frac{1}{a}$
0.0333 + 0.25 = $\frac{1}{17.143}$
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The RIGHT answer is
17.143 minutes.

Answer 2

There is a formula for this
Time = [Worker 1 * Worker 2] / [Worker 1 + Worker 2]
Time = 30*40 / (30+40)
Time = 1,200 / 70
Time = 17.1428571429 minutes

Alternate method
In 1 minute, Mark can clean (1/30) of a room
In 1 minute, Lynn can clean (1/40) of a room
Together, they can clean (1/30 + 1/40) = (7 / 120) of a room in 1 minute.
Together, they can clean one room in (120 / 7) minutes.
(120 / 7) =  17.1428571429 minutes.

Source:
http://www.1728.org/work.htm