Chapter 5, Problem 7PSP

To determine

To calculate the total time spent on painting the wall by brother, sister and myself by diagram and equation.

Answer to Problem 7PSP

1 hour

Explanation of Solution

Given:

Sister completes the paint in $2\text{}\text{hours}$ , brother completes the paint in $6\text{}\text{hours}$ and myself completes the paint in $3\text{}\text{hours}$

Formula used:

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

Calculation:

To calculate the time taken by all three of them it is needed to evaluate the rate of work and work done by all of them.

Let time (in hours) spend to wallpapering the wall is $t.$

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

  

The sum of brother work and sister’s work and self work equals to one whole wall painting.

Therefore, the equation obtained as:

  $\begin{array}{l}\Rightarrow \frac{t}{2}+\frac{t}{6}+\frac{t}{3}=1\\ \Rightarrow 12\times (\frac{t}{2}+\frac{t}{6}+\frac{t}{3})=1\times 12\\ \Rightarrow 6t+2t+4t=12\\ \Rightarrow 12t=12\\ \Rightarrow t=1\text{hour}\end{array}$

Diagram:

After one hour the wall is painted as follows,

  

Conclusion:

Hence, total 1 hour is spent to paint the wall by sister, brother and self.