https://file.aiquickdraw.com/mathbot/file/1726345196572t2r0gbem.jpg

Let's break down the problem from the image:

- **A** can do a job in \(7 \frac{1}{2}\) hours, which is equivalent to 7.5 hours.
- **B** is 20% more efficient than **A**.

We need to find how long it will take **B** to complete the same job.

### Step-by-Step Solution:
1. **Efficiency Relationship:**
   If **B** is 20% more efficient than **A**, then **B**'s efficiency is \(1.2 \times \text{Efficiency of A}\).

2. **Rate of Work:**
   The rate of work for **A** is \(\frac{1}{7.5}\) jobs per hour (since it takes 7.5 hours to complete 1 job).
   Therefore, **B**'s rate of work is:
   \[
   \text{Rate of B} = 1.2 \times \frac{1}{7.5} = \frac{1.2}{7.5} = \frac{12}{75} = \frac{4}{25} \text{ jobs per hour}.
   \]

3. **Time Taken by B:**
   The time taken by **B** to complete 1 job will be the reciprocal of **B**'s rate of work:
   \[
   \text{Time for B} = \frac{1}{\frac{4}{25}} = \frac{25}{4} = 6.25 \text{ hours}.
   \]
   This is \(6 \frac{1}{4}\) hours.

Thus, the correct answer is **option (D): 6 \(\frac{1}{4}\) hours**.

Would you like further clarification or details? Here are some related questions to consider:

1. What if B were only 10% more efficient than A?
2. How does changing the efficiency affect the time required to complete the job?
3. Can we calculate how much faster B finishes compared to A in terms of percentage?
4. If both A and B work together, how long will it take them to finish the job?
5. What happens if A's time to finish increases by 50%?

**Tip:** When efficiency is increased by a percentage, it directly affects the rate of work but inversely affects the time required to complete the task!

A can do a certain job in 7 1/2 hours. B is 20% more efficient than A. How many hours does B alone take to do the same job?

In this problem, A can complete a job in 7.5 hours, and B is 20% more efficient. Learn how to calculate how long it will take B to finish the same job using efficiency and work rate formulas. Suitable for Grades 8-10.

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