Question

an electric filter purifies air at the rate of 35 liters per minute and uses energy at the rate of 0.8 joules per minute. it also purifies water at the rate of 25 liters per minute and uses energy at the rate of 1.3 joules per minute.
the filter is expected to purify more than 1000 liters of air and water while using less than 170 joules of energy.
let ( a ) denote the number of minutes it spends purifying air and ( w ) the number of minutes it spends purifying water.
write an inequality that represents the condition based on the number of liters of air and water.
write an inequality that represents the condition based on the number of joules of energy.

Explanation:

First Sub - Question (Liters of Air and Water)

Step 1: Determine the amount of air and water

The rate of purifying air is 35 liters per minute, and the time spent purifying air is \(A\) minutes. So the amount of air purified is \(35A\) liters. The rate of purifying water is 25 liters per minute, and the time spent purifying water is \(W\) minutes. So the amount of water purified is \(25W\) liters.

Step 2: Write the inequality for total liters

The total liters of air and water is the sum of the liters of air and liters of water. The filter is expected to purify more than 1000 liters of air and water. So the inequality is \(35A + 25W>1000\).

Second Sub - Question (Joules of Energy)

Step 1: Determine the energy used for air and water

The energy used for purifying air is at a rate of 0.8 Joules per minute, and the time spent purifying air is \(A\) minutes. So the energy used for air is \(0.8A\) Joules. The energy used for purifying water is at a rate of 1.3 Joules per minute, and the time spent purifying water is \(W\) minutes. So the energy used for water is \(1.3W\) Joules.

Step 2: Write the inequality for total energy

The total energy used is the sum of the energy used for air and energy used for water. The filter is expected to use less than 170 Joules of energy. So the inequality is \(0.8A+1.3W < 170\).

Answer:

• For liters of air and water: \(35A + 25W>1000\)
• For joules of energy: \(0.8A + 1.3W<170\)