Can someone help with the problem shown in the image below: I want to measure th

Question

Can someone help with the problem shown in the image below:

I want to measure the amount of water that is piped into my neighborhood during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any given instant. I checked the gauge and the flow rate was about 100 cubic meters/hr at 6am. The flow rate increased steadily to about 280 cubic meters/hr at 9am. Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am. Include any tables or sketches in your solution.

Explanation / Answer

let rate of flow rate for the 3hrs vary as Q = mt + c at t = 0 , Q = 100 ==> c=100 at t =3 Q = 280 = 3m + 100 ==> m =60 total water flowed = intergral(60t+100)dt for t=0 to t=3 = 570

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