Chapter 8.6, Problem 11CYU

a.

To determine

To find : how much will Kendal complete 1 minute

Answer to Problem 11CYU

Kendal will complete the work in 1 minute is $\frac{1}{60}$

Explanation of Solution

Given information :

Kendal and Chandi wax cars. Kendal can wax a particular car in 60 minutes and Chandi can wax the same car in 80 minutes.

Calculation :

Kendal can wax a particular car in 60 minutes

Therefore, Kendal will complete the work in 1 minute $=\frac{1}{60}$

Hence, Kendal will complete the work in 1 minute is $\frac{1}{60}$ .

b.

To determine

To find : how much will Kendal complete $x$ minutes

Answer to Problem 11CYU

Kendal will complete the work in $x$ minutes is $\frac{x}{60}$

Explanation of Solution

Given information :

Kendal and Chandi wax cars. Kendal can wax a particular car in 60 minutes and Chandi can wax the same car in 80 minutes.

Calculation :

Kendal will complete the work in 1 minute is $\frac{1}{60}$

Therefore, Kendal will complete the work in $x$ minutes $=\frac{x}{60}$

Hence, Kendal will complete the work in $x$ minutes is $\frac{x}{60}$ .

c.

To determine

To find : how much will Chandi complete 1 minute

Answer to Problem 11CYU

Chandi will complete the work in 1 minute is $\frac{1}{80}$

Explanation of Solution

Given information :

Kendal and Chandi wax cars. Kendal can wax a particular car in 60 minutes and Chandi can wax the same car in 80 minutes.

Calculation :

Chandi can wax at the same car in 80 minutes

Therefore, Chandi will complete the work in 1 minute $=\frac{1}{80}$

Hence, Chandi will complete the work in 1 minute is $\frac{1}{80}$ .

d.

To determine

To find : how much will Chandi complete $x$ minutes

Answer to Problem 11CYU

Chandi will complete the work in $x$ minutes is $\frac{x}{80}$

Explanation of Solution

Given information :

Kendal and Chandi wax cars. Kendal can wax a particular car in 60 minutes and Chandi can wax the same car in 80 minutes.

Calculation :

Chandi will complete the work in 1 minute is $\frac{1}{80}$

Therefore, Chandi will complete the work in $x$ minutes $=\frac{x}{80}$

Hence, Chandi will complete the work in $x$ minutes is $\frac{x}{80}$ .

e.

To determine

To write : a rational equation representing Kendal and Chandi working together on the cax

Answer to Problem 11CYU

The equation of Kendal and Chandi working together on the car is $\begin{array}{l}\frac{x}{60}+\frac{x}{80}=1\end{array}$

Explanation of Solution

Given information :

Kendal and Chandi wax cars. Kendal can wax a particular car in 60 minutes and Chandi can wax the same car in 80 minutes.

Calculation :

Kendal will complete the work in $x$ minutes $=\frac{x}{60}$

Chandi will complete the work in $x$ minutes $=\frac{x}{80}$

Therefore, the rational equation representing Kendal and Chandi working together on the car is $\begin{array}{l}\frac{x}{60}+\frac{x}{80}=1\end{array}$

Hence, the equation of Kendal and Chandi working together on the car is $\begin{array}{l}\frac{x}{60}+\frac{x}{80}=1\end{array}$ .

f.

To determine

To solve : the equation to determine how long it will take them to finish the car

Answer to Problem 11CYU

It will take them to finish the car in $34.3\text{ minutes}$

Explanation of Solution

Given information :

Kendal and Chandi wax cars. Kendal can wax a particular car in 60 minutes and Chandi can wax the same car in 80 minutes.

Calculation :

The equation to determine is $\frac{x}{60}+\frac{x}{80}=1$

It will take them to finish the car.

  $\begin{array}{l}\frac{x}{60}+\frac{x}{80}=1\\ \frac{4x+3x}{240}=1\\ 7x=240\\ x=\frac{240}{7}\\ x=34.3\text{ minutes}\end{array}$

Hence, it will take them to finish the car in $34.3\text{ minutes}$ .