Solve each problem. See Examples 5 and 6. Formaldehyde is an indo...

Question

Solve each problem. See Examples 5 and 6. Formaldehyde is an indoor air pollutant formerly found in plywood, foam insulation, and carpeting. When concentrations in the air reach 33 micrograms per cubic foot (μg/ft^3), eye irritation can occur. One square foot of new plywood could emit 140 μg per hr. (Data from A. Hines, Indoor Air Quality & Control.) The room contains 800 ft^3 of air and has no ventilation. Determine how long it would take for concentrations to reach 33 μg/ft^3. (Round to the nearest tenth.)

Accepted Answer

Hello, today we're going to be solving the following word problem. So we are told that a new material was used on a wall of a room and this material is known to release toxic particles. The particles can cause sneezing if the concentration in the air reaches micrograms per cubic meter, one square meter of this material could release the particles at a rate of 120 micrograms per hour. And the room has 80 m squared of wall and 200 m cubed of air. We want to go ahead and calculate the time for the concentrations to reach micrograms per meters cubed. And we're going to express our answer to the nearest 10th. So let's go ahead and start this problem. Now, there's a few things to note of what is given to us. We are told that one square meter of the material used releases the particles at a rate of 120 micrograms per hour. And we are told that the room has 80 m squared of wall. So before we begin this problem, let's go ahead and come up with an equation which can represent the amount of particles released per hour by one m cubed. So we're going to let that BP. And since we are told that one m squared releases 100 and 20 micrograms per hour, we're going to represent that amount as 100 and 20 micrograms per hour per meter squared. That's going to be the amount of particles released by one m squared of wall. And we are told that there is a total of 80 m squared of wall in the room. So we're going to multiply that amount by 80 m squared. And since we don't know the amount of time it will take, we're going to represent time as X hours. So simplifying this hours and meters squared are going to cancel each other out. And what we are left with is 100 and 20 times 80 times X which is going to simplify to give us X. So what this represents is the rate at which the particles are being, being released per hour. And again, X represents the amount of hours that we want to find. Now, we want to go ahead and find the concentration needed for the sneezing to occur. So we are told that if the air reaches 900 micrograms per cubic meter, that's when the sneezing occurs. But we are also told that there are 200 m cubed of air in the room. So in order to figure out what the concentration needs to be in order to figure out when the sneezing starts, we're gonna multiply 900 micrograms per meters cubed by 200 by 200 m cubed And multiplying this together is going to give us 180,000 micrograms. So this is going to be the amount of micrograms needed to fill the room in order for the sneezing to occur. Now, since we want to find the amount of time it takes, in order to reach this amount, we're going to take our 9600 X And set it equal to 180,000 micrograms. And now we want to go ahead and sulfur X. Now, in order to solve for X, we're gonna divide both sides of this equation by 9600. And doing this is going to leave us with X is equal to 18.75 hours. And again, we want to represent our answer to the nearest 10th. So rounding this to the nearest 10th place is going to leave us with 18.8 hours. So that means it's going to take 18.8 hours for the room to have a total amount of 180,000 micrograms of this particles. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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