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?

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Solution

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 $t$ Hours
Total work is $t (\frac{1}{10} + \frac{1}{15})$ .
Lets represent total work by $1$ and calculate $t$ as shown:
$\begin{array}{rcl} t (\frac{1}{10} + \frac{1}{15}) & = & 1 \\ \Rightarrow & t (\frac{25}{150}) = 1 \\ \Rightarrow & t = \frac{150}{25} \\ \Rightarrow & t = 6 hours \end{array}$
Hence, Mr. Rose and John both complete the printing job in $6 Hours$

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