Math Problem Statement

Find out the answer

Arun can complete a task in 22 hours, and Bala can complete the same task in 6 hours. How much time will they take to finish the task if they work together?

Solution

I can help you solve the questions from the image. Let's go through each one individually:

13. Arun and Bala working together

Arun can complete a task in 22 hours, and Bala can complete the same task in 6 hours. How long will they take together?

We use the formula: Work rate=1time taken\text{Work rate} = \frac{1}{\text{time taken}}

So, for Arun: Work rate of Arun=122\text{Work rate of Arun} = \frac{1}{22} For Bala: Work rate of Bala=16\text{Work rate of Bala} = \frac{1}{6}

When they work together, the combined work rate is the sum of their individual rates: Combined rate=122+16\text{Combined rate} = \frac{1}{22} + \frac{1}{6}

1Total Time=122+16\frac{1}{\text{Total Time}} = \frac{1}{22} + \frac{1}{6}

Now, let me calculate this.

The total time taken for Arun and Bala to complete the task together is 337\frac{33}{7} hours, which is approximately 4.7 hours.

Thus, the answer to question 13 is: A. 4.7 hours

Would you like me to solve the next question? Feel free to ask for clarifications or more details.

Here are 5 related questions to practice:

  1. How do you calculate work rates when multiple workers are involved?
  2. If another person could do the same task in 8 hours, how would the total time change?
  3. How would the formula change if the workers had different efficiency levels for different parts of the task?
  4. How does dividing the work among multiple people reduce the overall time?
  5. Can the total time ever exceed the time taken by the slowest person?

Tip: When solving work-related problems, always sum up the rates to get the combined rate, and take the reciprocal to find the total time.

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Math Problem Analysis

Mathematical Concepts

Work-Rate Problems
Fractions
Time and Efficiency

Formulas

Work rate = 1 / (time taken)
Combined work rate = sum of individual rates
Total time = 1 / (combined rate)

Theorems

Basic work-rate theorem
Reciprocal theorem in work problems

Suitable Grade Level

Grades 8-10