Chapter 11.6, Problem 40PPE

To determine

To calculate time that how long would take 5 people to paint the house.

Answer to Problem 40PPE

  $k=\frac{12}{5}$

Explanation of Solution

Given:

Given

  $\begin{array}{l}time=3days\\ people=4\\ by5people=?\end{array}$

Concept Used:

• Efficiency × time = work

Calculation:

In order to solve the question and find the work, we have given efficiency, time

  $\begin{array}{l}time=3days\\ efficiency=4\end{array}$

  $\begin{array}{l}work=efficiencyofpeople\times time\\ work=4\times 3\\ =12\\ andfor5people\\ time=\frac{work}{efficiency}\\ =\frac{12}{5}days\end{array}$

(1) This equation represents direct variation,

As we know that in direct variation $y\propto x$ or $y=kx$

Work represents $y$ , efficiency represents $x$ and time (i.e. $\frac{12}{5}$ ) represents k constant of variation

Hence it is direct variation.

(2) We can write an equation with the help of 1^st part as given

  $\begin{array}{l}\frac{work}{efficiency}=time\\ \frac{y}{x}=k\\ \frac{y}{x}=\frac{12}{5}\end{array}$

Thus, the solution is correct.