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Corinne S.

asked • 09/11/18

Will the rainwater tank fill up?

A huge storm is quickly filling up Manuel’s rainwater collection tank. Manuel wants to know if his 1000 gallon tank will overflow in the next hour, so he uses a rain gauge to determine that rain water is filling up his tank at a rate of 0.5t gallons per minute.
If Manuel’s predicted rate is correct, will his rainwater tank overflow within the hour?

Corinne S.

If I do a sum of a sequence, I get .5 + 1 + 1.5 .... + 30
 
60/2(.5+30) = 915
 
But if I do area under the linear equation, I get 900. 
 
Why are they different?
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09/11/18

1 Expert Answer

By:

Corinne S.

his rate is increasing! That is exactly what is happening. 
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09/11/18

David W.

tutor
The rate is constant at 0.5 inches per minute
 
After 1 minute 0.5 inches are added to the tank.
 
After 2 minutes, another 0.5 inches is added to the tank for a total of 1 inch in the tank.
 
After 3 minutes, another 0.5 inches is added and there is 1.5 inches in the tank.
 
By doing sum of sequence, you are saying the the amount of water filling the tank is increasing every minute. Instead, the rate of the filling is steady but the volume of the rain in the tank is increasing.
 
Let's look at another example. If I walk 2 mph, after 3 hours, I walk 2 + 2 + 2 = 2(3) = 6 miles.
 
If I increase my speed by 1 mph every hour, my distance walked is not linear because the my speed is not constant, and I will have walked farther.
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09/11/18

Corinne S.

You are incorrect. it specifically says that the rate is changing linearly
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09/12/18

David W.

tutor
Corinne, please see your teacher. You have a gross misunderstanding of the concept.
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09/12/18

Corinne S.

Ha ha. I am a teacher. I needed help in explaining this without using Calculus. I am Not misunderstanding the concept. however there were some parts that I did not incl in the question. It was a miscommunication but I figured it out on my own. Thanks anyway. Oh and the answer is 900 gallons. 
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09/13/18

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