Question

Sue can clean the room in 45 minutes. Ann can clean the room in 1 hour. Sue cleaned for 15 minutes before Ann came to help her. How long did they work together to finish cleaning? Write answer in fraction then write in decimal.

Answer 1

They will work for
`17(1)/(7)` minute
`\simeq 17.14` minute together to finish the work.

Explanation:

In 45 minutes Sue cleans the whole room

So, in 1 minute Sue does
`\frac {1}{45}` part of the total work -------(1)

so in 15 minutes Sue does
`\frac {1 * 15}{45}`

=
`\frac {1}{3}` part of the total work -------------------------(2)

So, the amount of work left, = (1 - 1/3)

= 2/3 of the total work.

In 60 minutes, Ann cleans the whole room

so,in 1 minute Ann does
`(1)/(60)` of the total work.

So, in 1 minute, Ann and Sue together do,

`(1)/(45) +(1)/(60)`

=
`(4 + 3)/(180)`

=
`\frac {7}{180}` of the total work.

So, Ann and Sue together do
`\frac {7}{180}` of the total work in 1 minute.

So, they would have done the whole work in,
`\frac {180}{7}` minute.

So, they would do
`(2)/(3)` of the total work in

`(180 * 2)/(3 * 7)` minute

=
`(120)/(7)` minute

=
`17(1)/(7)` minute

`\simeq 17.14` minute