Question

It takes Mr. Rose $10$ hours to complete a printing job.

His helper John can complete the same job in $15$ hours.

If Mr. Rose and John work together, how long will it take them to complete the job?

Answer 1

Finding the time For Both Mr. Rose and John to complete the job :

According to Question Rose Complete work in $10$hours .

John Complete Work in $15$ hours.

Work Done by Mr. Rose Per Hour is $\frac{1}{10}$of total work.

Work Done by John per Hour is $\frac{1}{15}$of total work.

Now Let's Assume They complete Work in $\mathrm{t}$ Hours

Total work is $\mathrm{t}\left(\frac{1}{10}+\frac{1}{15}\right)$.

Lets represent total work by $1$ and calculate $t$ as shown:

$\begin{array}{rcl}\mathrm{t}\left(\frac{1}{10}+\frac{1}{15}\right)& =& 1\\ & \Rightarrow & \mathrm{t}\left(\frac{25}{150}\right)=1\\ & \Rightarrow & \mathrm{t}=\frac{150}{25}\\ & \Rightarrow & \mathrm{t}=6\mathrm{hours}\end{array}$

Hence, Mr. Rose and John both complete the printing job in $6\mathrm{Hours}$