Chapter 1.9, Problem 21P

To determine

To calculate:

The original rate of an emission of pollutant in the exhaust of the car:

Answer to Problem 21P

The original rate of an emission of pollutant is $80$ ppm.

Explanation of Solution

Given information:

Total rate of emission of air pollutant in car’s exhaust: $56$ ppm

Calculation:

Let, the original rate of an emission be $x$ . Thus, the reduced rate of an emission is $x-56$ :

The equation relating the original rate of the pollution and reduced rate:

  $3x=10\left(x-56\right)\mathrm{...}\left(1\right)$

Subtract from both the sides in this equation (1)

  $\begin{array}{l}3x-10x=10x-10x-560\\ -7x=-560\end{array}$

Divide both the sides by $-7$ :

  $\begin{array}{l}\therefore \frac{-7}{-7}t=\frac{-560}{-7}\\ \therefore x=80\end{array}$

The original rate of an emission is $80$ ppm.

Put $80$ for $x$ in $x-56$

  $\begin{array}{l}\left(x-56\right)=80-56\\ \left(x-56\right)=24\end{array}$

The reduced rate of emission is $24$ ppm.

The difference in the original rate and reduced rate of pollution:

  $\begin{array}{l}80-24=56\\ 56=56\end{array}$

The original rate of an emission of pollutant is $80$ ppm.