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.

Accepted Solution

Answer:They will work for [tex]17\dfrac{1}{7}[/tex] minute [tex]\simeq 17.14[/tex] minute  together to finish the work.Step-by-step explanation:In 45 minutes Sue cleans the whole roomSo, in 1 minute Sue does [tex]\frac {1}{45}[/tex] part of the total work -------(1)so in 15 minutes Sue does [tex]\frac {1 \times 15}{45}[/tex]                     = [tex]\frac {1}{3}[/tex] 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 roomso,in 1 minute Ann does [tex]\frac{1}{60}[/tex] of the total work.So, in 1 minute, Ann and Sue together do,                                                     [tex]\frac{1}{45} +\frac{1}{60}[/tex]                                                     = [tex]\frac{4 + 3}{180}[/tex]                                                     = [tex]\frac {7}{180}[/tex]  of the total work.So, Ann and Sue together do [tex]\frac {7}{180}[/tex]  of the total work in 1 minute.So, they would have done  the whole work in, [tex]\frac {180}{7}[/tex] minute.So, they would do [tex]\frac{2}{3}[/tex] of the total work in   [tex]\frac{180 \times 2}{3 \times 7}[/tex] minute   = [tex]\frac{120}{7}[/tex] minute   = [tex]17\dfrac{1}{7}[/tex] minute   [tex]\simeq 17.14[/tex] minute