Chapter 7.4, Problem 55E

(a)

To determine

To find: The expression for the rates at which the employee was the car.

Answer to Problem 55E

Thus, the rate of the first employee is $R_1=\frac{1}{40}$ , the second employee is $\frac{1}{x}$ and the rate of the third employee is $R_3=\frac{1}{x+10}$ .

Explanation of Solution

Given:

The average time taken to wash the car by one employee is 40 minutes.

The time taken to wash the car by other employee is $x$ minutes.

The time taken by the third employee to wash the car is $x+10$ .

Calculation:

Consider the average of the time taken to wash the car by the first employee is,

  $R_1=\frac{1}{40}$

The second employee wash the car in $x$ minutes is,

  $R_2=\frac{1}{x}$

The rate at which the third employee was the car is,

  $R_3=\frac{1}{x+10}$

Thus, the rate of the first employee is $R_1=\frac{1}{40}$ , the second employee is $\frac{1}{x}$ and the rate of the third employee is $R_3=\frac{1}{x+10}$ .

(b)

To determine

To find: The combined rate of cars washed per minute by the group.

Answer to Problem 55E

Thus, the combined rate to wash the car is $\frac{x^2+90x+400}{40x\left(x+10\right)}$ .

Explanation of Solution

Given:

The average time taken to wash the car by one employee is 40 minutes.

The time taken to wash the car by other employee is $x$ minutes.

The time taken by the third employee to wash the car is $x+10$ .

Calculation:

From part (a), the combined rate for washing the car by all the employee is,

  $\begin{array}{c}R=\frac{1}{x}+\frac{1}{40}+\frac{1}{x+10}\\ =\frac{x\left(x+10\right)}{40x\left(x+10\right)}+\frac{40\left(x+10\right)}{40x\left(x+10\right)}+\frac{40x}{40x\left(x+10\right)}\\ =\frac{x^2+90x+400}{40x\left(x+10\right)}\end{array}$

(c)

To determine

To find: The number of cars washed per hour by the second employee.

Answer to Problem 55E

Thus, the rate at which the car is washed is $0.0758$ cars per minute that is 4.5 cars per hour.

Explanation of Solution

Given:

The time taken to was the car by second employee is $35$ minutes.

Calculation:

Consider the combined rate of washing the car is,

  $R=\frac{x^2+90x+400}{40x\left(x+10\right)}$

Then,

  $\begin{array}{c}R=\frac{{\left(35\right)}^2+90\left(35\right)+400}{40\left(35\right)\left(35+10\right)}\\ =\frac{4775}{63,000}\\ =0.0758\end{array}$

Thus, the rate at which the car is washed is $0.0758$ cars per minute that is 4.5 cars per hour.