Question 1178476
Let's break down this problem step by step:

**(a) Equation for Total Ventilation (V)**

* **Ventilation per person:** 15 ft³/min
* **Number of students:** x
* **Total ventilation per minute:** 15x ft³/min
* **Convert to cubic feet per hour:** 15x ft³/min * 60 min/hour = 900x ft³/hour

Therefore, the equation is:
* **V = 900x**

**(b) Air Exchanges per Hour (A)**

* **Total ventilation per hour:** V = 900x ft³/hour
* **Classroom volume:** 15,000 ft³
* **Air exchanges per hour (A):** A = (Total ventilation per hour) / (Classroom volume)
* **A = (900x) / 15,000**
* **A = 9x / 150 = 3x / 50**

Therefore, the number of air exchanges per hour is:
* **A = 3x / 50**

**(c) Necessary Air Exchanges with 40 Students**

* **Number of students (x):** 40
* **A = 3x / 50**
* **A = 3(40) / 50**
* **A = 120 / 50**
* **A = 12 / 5 = 2.4**

Therefore, with 40 students, 2.4 air exchanges per hour are necessary.

**(d) Ventilation Increase in Smoking Areas**

* **Ventilation in classrooms:** 15 ft³/min per person
* **Ventilation in smoking areas:** 50 ft³/min per person
* **Factor increase:** (Ventilation in smoking areas) / (Ventilation in classrooms)
* **Factor increase:** 50 / 15
* **Factor increase:** 10 / 3 ≈ 3.33

Therefore, ventilation should be increased by a factor of 10/3 or approximately 3.33 in heavy smoking areas.