A robot can complete 7 tasks in three fourths

Question

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.)

Answer 1

To solve the problem, we can break it down into two parts.

Part a: How long does it take the robot to complete one task?

The robot completes 7 tasks in $\frac{3}{4}$ hour.

To find out how long it takes to complete one task, we divide the total time it takes for 7 tasks by the number of tasks:

$$\text{Time per task}=\frac{\text{Total time}}{\text{Number of tasks}}=\frac{\frac{3}{4}\text{ hour}}{7}$$

Calculating this gives:

$$\text{Time per task}=\frac{3}{4}÷7=\frac{3}{4}\times \frac{1}{7}=\frac{3}{28}\text{ hour}$$

So, it takes the robot $\frac{3}{28}$ hour to complete one task.

Part b: How many tasks can the robot complete in one hour?

To find out how many tasks the robot can complete in one hour, we can find the rate of tasks completed per hour.

Since the robot completes 7 tasks in $\frac{3}{4}$ hour, we can use this to calculate the number of tasks completed in one hour:

$$\text{Number of tasks in 1 hour}=7÷\frac{3}{4}$$

Calculating this gives:

$$\text{Number of tasks in 1 hour}=7\times \frac{4}{3}=\frac{28}{3}\approx 9.33$$

Thus, the robot can complete approximately 9.33 tasks in one hour, or more accurately, 9 full tasks (since it cannot complete a fraction of a task).

So to summarize:

• a. It takes the robot $\frac{3}{28}$ hour to complete one task.
• b. The robot can complete 9 full tasks in one hour.