Question

Mia and Holly can clean their room in 20 min, working together. Mia, working alone, can do the job in 30 min. How many minutes will it take Holly to
clean their room, working alone?

A 30

B. 60

C. 50

D. 80

Answer 1

Answer:

Option B. is correct

Step-by-step explanation:

Let $x$ denotes time taken by Mia alone to clean the room and $y$ denotes time taken by Holly alone to clean the room.

As Mia and Holly can clean their room in 20 min, working together,

$\frac{1}{x}+\frac{1}{y} =\frac{1}{20}\,\,\,...(i)$      

Also,

Mia, working alone, can do the job in 30 min.

So,

$\frac{1}{x}=\frac{1}{30}\,\,\,\,\,...(ii)$

Put (ii) in (i)

$\frac{1}{30}+\frac{1}{y}=\frac{1}{20}\\\frac{1}{y}=\frac{1}{20}-\frac{1}{30}\\\frac{1}{y}=\frac{3-2}{60} \\\frac{1}{y}=\frac{1}{60}$

Therefore,

Holly can clean the room alone in 60 minutes.

Option B. is correct