Question

A robot can complete 5 tasks in two thirds 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? A. It takes the robot nothing ​hour(s) to complete one task. ​(Simplify your​ answer.)

Answer 1

Answer:

It'll take the robot 8 minutes to complete one task

7.5 tasks will be completed in one hour

Step-by-step explanation:

Total time to complete 5 tasks is 2/3hr (40 minutes)

Time it takes to complete one task = 40 ÷ 5 = 8 minutes

Since the robot completes one task in 8 minutes, x tasks will be completed in 60 minutes.

x = 60 ÷ 8 =  7.5 tasks

Answer 2

Answer:

A. 8 minutes; B. 7.5 tasks in one hour; C. It takes the robot about $\\ \frac{2}{15}\;hour$ or about 0.1333 hour to complete one task or 13.33% of one hour.

Step-by-step explanation:

Part A

Two thirds hours is

$\\ \frac{2}{3}*60 = 40\;min$  

We know that each task takes the same amount of time. So, 40min can be divided by 5:

$\\ \frac{40}{5} = 8\;min$

Thus, each task takes 8 min to be completed. Then, it takes the robot 8 minutes to complete one task.

Part B

The robot can complete 5 tasks in 40 minutes, how many tasks can the robot complete in 60 minutes or one hour?

There are 20 minutes ahead to complete one hour. In the next 8 minutes, the robot can complete one task. There are still 12 minutes ahead. In the next 8 minutes, the robot completes another task. There is still 4 minutes ahead to complete the hour, but in 4 minutes the robot can complete half of the task because it takes 8 minutes for a complete task. Therefore, the robot can complete 5 tasks + 2 tasks + 0.5 task = 7.5 tasks in one hour or 60 minutes.

We can obtain the same answer using proportions. That is, if 5 tasks are completed in 40 minutes, how many of them will be completed in one hour or 60 minutes.  

Then

$\\ \frac{5\;tasks}{40\;min} = \frac{x}{60\;min}$

$\\ \frac{5\;tasks}{40\;min}*60\;min = x$

$\\ x = \frac{5\;tasks*60\;min}{40\;min}$

$\\ x = \frac{300\;tasks}{40} = 7.5\;tasks$

Part C (A)

From part A, we already know that the robot can complete a task in 8 minutes, which is a fraction of one hour. What is this fraction? In one hour we have 60 minutes, then

$\\ 8\;min*\frac{1\;hour}{60\;min} = 1\;hour*\frac{8}{60} = 1\;hour*\frac{4}{30} = 1\;hour*\frac{2}{15} = 0.1333333....\;hours \approx 0.1333\;hours$.

Therefore, it takes the robot about $\\ \frac{2}{15}\;hour$ or 0.1333 hour to complete one task (rounding to four decimal places) or 13.33% of one hour.