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

Answer:

They will work for $17\dfrac{1}{7}$ minute $\simeq 17.14$ minute  together to finish the work.

Step-by-step 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 $\frac {1 \times 15}{45}$

                    = $\frac {1}{3}$ 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 $\frac{1}{60}$ of the total work.

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

                                                    $\frac{1}{45} +\frac{1}{60}$

                                                    = $\frac{4 + 3}{180}$

                                                    = $\frac {7}{180}$  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 $\frac{2}{3}$ of the total work in

  $\frac{180 \times 2}{3 \times 7}$ minute

  = $\frac{120}{7}$ minute

  = $17\dfrac{1}{7}$ minute

  $\simeq 17.14$ minute