mahesh  does a piece of work in 8 hours . Mohan does a piece of work in 6 hours , If they work together then how many they will do this

To find out how long it will take Mahesh and Mohan to complete the work together, we can use the concept of work rates.

- Mahesh's rate of work: \( \frac{1}{8} \) of the work per hour.
- Mohan's rate of work: \( \frac{1}{6} \) of the work per hour.

When they work together, their combined work rate is the sum of their individual work rates:
\[
\text{Combined work rate} = \frac{1}{8} + \frac{1}{6}
\]

To add these fractions, first find a common denominator:
\[
\frac{1}{8} + \frac{1}{6} = \frac{3}{24} + \frac{4}{24} = \frac{7}{24}
\]

So, their combined work rate is \( \frac{7}{24} \) of the work per hour.

To find the time it takes for them to complete the work together, divide 1 (the whole work) by their combined work rate:
\[
\text{Time taken} = \frac{1}{\frac{7}{24}} = \frac{24}{7} \text{ hours} \approx 3.43 \text{ hours}
\]

So, it will take them approximately 3.43 hours to complete the work together.

Would you like further details or have any questions?  

Here are 5 related questions:

1. How do you calculate individual work rates?
2. What is the formula for combined work rates?
3. How would the time change if Mahesh worked faster?
4. How can you convert the final time into minutes?
5. What if a third person joins in? How would that affect the time?

**Tip:** Always make sure to find a common denominator when adding fractions involving different work rates.

Learn how to calculate work rates when Mahesh and Mohan work together to complete a task. Understand the concept of combined work rates and how to compute the time required for them to finish the work. Suitable for Grades 7-9 students learning about rates of work and fractions.

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