Question

Sita can finish typing a $100-\text{page document}$ in $9$ hours, Mita in $6$ hours and Rita in $12$ hours. How long will they take to type a $100-\text{page document}$ if they work together $?$

Answer 1

Step: Find the time required to type a $100-\text{page document}$

Given:
Time taken by Sita to finish the work $=9$ hours
Time taken by Mita to finish the work $=6$ hours
Time taken by Rita to finish the work $=12$ hours

So,
Amount of work done by Sita in $1\text{hour}=\frac{1}{9}$
Amount of work done by Mita in $1\text{hour}=\frac{1}{6}$
Amount of work done by Rita in $1\text{hour}=\frac{1}{12}$
Work done by Sita, Mita and Rita together in $1\text{hour}=\frac{1}{9}+\frac{1}{6}+\frac{1}{12}$
$=\frac{4+6+3}{36}$
$=\frac{13}{36}$

Hence , time taken by all Sita, Mita, and Rita together to type $100-\text{page document}=\frac{1}{\frac{13}{36}}\text{hours}$
$=\frac{36}{13}\text{hours}$

Hence , time taken by all Sita, Mita, and Rita together to type $100-\text{page document}$ is $\frac{36}{13}\text{hours}$