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

`(1)/(30)` +
`(1)/(40)` =
`(1)/(a)`
Multiply both sides by 120a
4a + 3a = 120
7a = 120
a = 17.143
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CHECK YOUR ANSWER:

`(1)/(30)` +
`(1)/(40)` =
`(1)/(a)`
0.0333 + 0.25 =
`(1)/(17.143)`
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The RIGHT answer is
17.143 minutes.