Chapter 5.6, Problem 36PS

Solution

a.

To calculate: Find the work done and complete the table.

	Work rate	Time	Work done
You	$\frac{1\text{ room}}{8\text{hour}}$	$5\text{hour}$	$\frac{5}{8}\text{room}$
Friend	$\frac{\text{3 room}}{40\text{hour}}$	$5\text{hour}$	$\frac{3}{8}\text{room}$

Given information:

You can paint the room in $8\text{hour}$ .

Friend can paint the room in $5\text{hour}$ .

Concept used:

  $workrate\times time=workdone$

Calculation:

By apply: $workrate\times time=workdone$

	Work rate	Time	Work done
You	$\frac{1\text{ room}}{8\text{hour}}$	$5\text{hour}$	$\frac{5}{8}\text{room}$
Friend	$\frac{\left(\frac{3}{8}\right)}{5}=\frac{\text{3 room}}{40\text{hour}}$	$5\text{hour}$	$\frac{3}{8}\text{room}$

b.

To calculate: The sum of work done from last column of table.

The sum of work done is $1\text{ room}$ .

Given information:

You can paint the room in $8\text{hour}$ .

Friend can paint the room in $5\text{hour}$ .

Concept used:

  $\text{work}\text{rate}\times \text{time}=\text{work}\text{done}$

Calculation:

The sum of the work done:

  $\frac{5}{8}+\frac{3}{8}=1$

Conclusion:

The sum of work done is $1\text{ room}$ .

c.

To calculate: Find how long friend would take to paint the room when working alone.

  $t=13\text{hr }20\text{min}$

Given information:

You can paint the room in $8\text{hour}$ .

Friend can paint the room in $5\text{hour}$ .

Concept used:

  $\text{work}\text{rate}\times \text{time}=\text{work}\text{done}$

Calculation:

The friend's rate is $3\text{rooms}$ per $8\text{hours}$ , so if time $t$ is how long it takes for $1\text{room}$ and the rate is the same so,

  $\begin{array}{l}\frac{1\text{room}}{t}=\frac{3\text{room}}{40\text{hr}}\\ 3t=40\\ t=\frac{40}{3}\\ =13.33\text{hr}\\ =13\text{hr}20\text{min}\end{array}$

Conclusion:

  $t=13\text{hr}20\text{min}$