# Algebra word problem

• Aug 13th 2010, 03:25 PM
sahip
Algebra word problem
A pollution control device reduces the rate of emission of an air pollutant in a car's exhaust by 56 parts per million per hour. When the device is installed, it will take the car 10 hr to emit the same amount of pollutant that it formerly did in 3 hr. What was the original rate of emission of the pollutant in the car's exhaust ?

Thank you.
(Happy)
• Aug 13th 2010, 05:22 PM
Soroban
Hello, sahip!

Quote:

A pollution control device reduces the rate of emission of an air pollutant
. . in a car's exhaust by 56 parts per million per hour.
When the device is installed, it will take the car 10 hr to emit the same amount
. . of pollutant that it formerly did in 3 hr.

What was the original rate of emission of the pollutant in the car's exhaust?

Let $\displaystyle ppm$ = parts per million.

Let $\displaystyle x$ ppm/hr = engine's original rate of emission of pollutant.

In 3 hours, it emits $\displaystyle 3x$ ppm of pollutant.

With the device installed, the engine's rate is: $\displaystyle x-56$ ppm/hr

In 10 hours, it emits $\displaystyle 10(x-56)$ ppm of pollutant.

These two amounts are equal: .$\displaystyle 10(x-56) \:=\:3x$

. . $\displaystyle 10x - 560 \:=\:3x \quad\Rightarrow\quad 7x \:=\:560 \quad\Rightarrow\quad x \:=\:80$

Therefore, the original rate of pollutant emission is $\displaystyle 80$ ppm/hr.