To solve this problem, let's break it down into two parts:

Part (a): Time to Complete One Task

The robot can complete 77 tasks in $\frac{2}{3}$ of an hour. We need to find out how long it takes the robot to complete one task.

1. First, calculate the time per task by dividing the total time by the number of tasks: $\text{Time per task} = \frac{\frac{2}{3} \text{ hour}}{77}$

2. Simplify the fraction: $= \frac{2}{3} \div 77 = \frac{2}{3} \times \frac{1}{77} = \frac{2}{231}$

3. So, it takes the robot $\frac{2}{231}$ hour to complete one task.

Part (b): Tasks Completed in One Hour

Now, let's find out how many tasks the robot can complete in one hour.

1. To do this, divide 1 hour by the time it takes to complete one task: $\text{Tasks per hour} = \frac{1}{\frac{2}{231}} = 1 \times \frac{231}{2} = 115.5$

2. Therefore, the robot can complete 115.5 tasks in one hour.

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Final Answers

• (a) It takes the robot $\frac{2}{231}$ hour(s) to complete one task.
• (b) The robot can complete 115.5 tasks in one hour.

Would you like further clarification on any part?

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Follow-Up Questions

1. How would the answers change if the robot took only $\frac{1}{3}$ hour to complete 77 tasks?
2. What is the time to complete 100 tasks at this rate?
3. If the robot's speed is halved, how long will it take to complete one task?
4. How many tasks can it complete in two hours?
5. What if the robot needs to complete 200 tasks? How long will that take?

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Quick Tip

Remember that dividing by a fraction is equivalent to multiplying by its reciprocal.