Chapter 5, Problem 9PSP

To determine

To find the time taken by two groups of students to wash $30\text{cars}$ .

Answer to Problem 9PSP

2.4 hours

Explanation of Solution

Given:

One group of students wash $\text{6 cars}\text{per hour}$ and other group wash $4\text{cars}\text{per hour}\text{.}$

Calculation:

To evaluate the time taken to wash the cars, calculate the total number of cars washed in one hour.

Work rate of group A in one hour $=\frac{1}{6}.$

Work rate of group B in one hour $=\frac{1}{4}.$

Let x be the time taken to wash 30 cars.

Work rate to wash 30 cars $=\frac{1}{x}.$

Therefore, time taken in car wash is obtained as:

  $\begin{array}{l}\Rightarrow \frac{1}{x}=\frac{1}{6}+\frac{1}{4}\\ \Rightarrow \frac{1}{x}=\frac{6+4}{6\times 4}\\ \Rightarrow \frac{1}{x}=\frac{10}{24}\\ \Rightarrow 1\times 24=10\times x\\ \Rightarrow 24=10x\\ \Rightarrow x=\frac{24}{10}\\ \Rightarrow x=2.4\text{hours}\end{array}$

Conclusion:

Hence, $2.4\text{hours}$ are taken to wash cars by both groups of students.