
Worker A takes 8 hrs to do a job. Worker B takes 10 hrs to do the same job. How long should it

take for both A and B, working together but independently to do the same job?

Let's solve the problem step by step.

### Step 1: Determine the work rates of A and B.
- Worker A takes 8 hours to complete the job. Therefore, A's work rate is \( \frac{1}{8} \) of the job per hour.
- Worker B takes 10 hours to complete the job. Therefore, B's work rate is \( \frac{1}{10} \) of the job per hour.

### Step 2: Combine the work rates of A and B.
- When A and B work together, their combined work rate is the sum of their individual work rates:
\[
\text{Combined rate} = \frac{1}{8} + \frac{1}{10}
\]

### Step 3: Find a common denominator and add the fractions.
- The common denominator for 8 and 10 is 40.
\[
\frac{1}{8} = \frac{5}{40}, \quad \frac{1}{10} = \frac{4}{40}
\]
\[
\text{Combined rate} = \frac{5}{40} + \frac{4}{40} = \frac{9}{40}
\]

### Step 4: Determine the time required for both A and B to complete the job together.
- Since the combined work rate is \( \frac{9}{40} \) of the job per hour, the time \( T \) required to complete the job is the reciprocal of the combined work rate:
\[
T = \frac{1}{\frac{9}{40}} = \frac{40}{9} \text{ hours}
\]

### Step 5: Simplify the result.
- \( \frac{40}{9} \) hours is approximately \( 4.44 \) hours.

### Final Answer:
It should take both A and B, working together but independently, **approximately 4.44 hours** to complete the job.

Would you like more details or have any questions?

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Here are 5 related questions for further practice:

1. If Worker A takes 6 hours and Worker B takes 12 hours to do a job, how long will it take them to do it together?
2. If Worker A can do a job in 7 hours and Worker B can do it in 14 hours, how much time will they take together?
3. If Worker C can do a job in 5 hours and Worker D in 20 hours, how long will it take them to complete the job together?
4. If three workers, A, B, and C, take 6 hours, 8 hours, and 12 hours respectively to do a job, how long will they take to complete it together?
5. If Worker A and Worker B work together for 3 hours and complete half the job, how much longer will it take them to finish the job if A works alone for 1 more hour?

**Tip:** When adding rates, it's crucial to first find a common denominator, which simplifies the arithmetic and leads to accurate results.

Discover how long it takes for workers A and B to complete a job individually and together. Learn the rates of work concept and its application to solve problems. Suitable for Grades 7-9.

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