Question

A robot can complete 5 tasks in 3/4 hour. Each task takes the same amount of time

Answer 1

a) A robot can complete 5 tasks in 3/4 hours

If it takes the same amount of time to complete each task

Let the time taken to complete one task be x

To complete 5 tasks,

`5* x=5x`

The time taken to complete the 5 tasks can be expressed below as

`5x=(3)/(4)\text{ hours}`

To find the time taken to complete one task, x,

Crossmultiply

`\begin{gathered} 5x=(3)/(4) \\ \text{Crossmultiply} \\ 5x*4=3 \\ 20x=3 \\ \text{Divide both sides by 20} \\ (20x)/(20)=(3)/(20) \\ x=(3)/(20)\text{hours} \end{gathered}`

Hence, it takes the robot 3/20 hours to complete one task

b) If the robot can complete one task in 3/20 hours,

Let the number of task(s) the robot can complete in one hour be k

The number of task(s) the robot can complete in one hour is

`\begin{gathered} If\text{ 1 task takes }(3)/(20)hours \\ \text{Number of task that can be completed in 1 hour will be,} \\ k*(3)/(20)=1*1 \\ (3k)/(20)=1 \\ \text{Crossmultiply} \\ 3k=1*20 \\ 3k=20 \\ \text{Divide both sides by 3} \\ k=(20)/(3) \\ k=6(2)/(3)\text{ tasks} \end{gathered}`

Hence, the robot can complete 6 2/3 tasks in one hour