A robot can complete

77

tasks in

two thirds23

hour. Each task takes the same amount of time.

**a.** How long does it take the robot to complete one​ task?

**b.** How many tasks can the robot complete in one​ hour?

Question content area bottom

Part 1

**a.** It takes the robot

enter your response here

​hour(s) to complete one task.

​(Simplify your​ answer.)

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.

---

### 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?

---

### 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?

---

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

A robot can complete 77 tasks in two-thirds of an hour. Each task takes the same amount of time.

**a.** How long does it take the robot to complete one task?

**b.** How many tasks can the robot complete in one hour?

Find out how long it takes a robot to complete one task given that it completes 77 tasks in two-thirds of an hour. Learn the step-by-step solution involving rate calculations, including time per task and tasks per hour. Suitable for students in Grades 6-8.

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