Question

Maria can rearrange all the furniture in the house in two hours. Her sister, Sasha, can rearrange all the furniture in the house in three hours. How long would it take for two of them to do the job together?

Answer 1

Answer: $1\frac{1}{5}$ hours

Step-by-step explanation:

Given: Time taken by Maria to rearrange the furniture in the house (M)= 2 hours

Time taken by Sasha to rearrange the furniture in the house (S)= 3 hours

Let t be the time taken by them if they work together.

$\\\Rightarrow\frac{1}{t}=\frac{1}{M}+\frac{1}{S}\\\\\Rightarrow\frac{1}{t}=\frac{1}{2}+\frac{1}{3}\\\\\Rightarrow\frac{1}{t}=\frac{3+2}{6}=\frac{5}{6}\\\\\Rightarrow\ t=\frac{6}{5}=1\frac{1}{5}$

Hence, if they work together then time taken by them would be $1\frac{1}{5}$ hours.