MATH SOLVE

4 months ago

Q:
# 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

A:

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