A town maintains a reservoir to provide drinking water to its citizens. While th

Question

A town maintains a reservoir to provide drinking water to its citizens. While the reservoir holds 52,000,000 m3, the water level is quite low (41,000,000 m3) after a dry season. Then, a large and growing rainstorm engulfs the town for 29 hours. The rate of rainfall can be approximated as 6930-t (m3/hr), where t(hr) is the time after the rain begins. Determine the expression for the volume of water in the reservoir as a function of time. Format your answer as fraction numerator d V over denominator d t end fraction equals f left parenthesis t right parenthesis Calculate the volume of water (m3) in the reservoir after the rain storm. The rainstorm now continues indefinitely past 29 hours. How many more hours until it overflows? As mentioned in original problem statement, the reservoir is relatively low this year. In a typical year, the reservoir would overflow from this 29 hours rainstorm. What is the usual volume of the reservoir?

Explanation / Answer

1) dV/dt =f = 6930

Volume of water = 41,000,000 + 6930*t

2) after rainstorm

V = 41,000,000 + 6930*29 = 41200970

3) t = t* at which V = 52,000,000

52,000,000 =  41200970+ 6930*t*

t* = 98173/63 = 1558.3015 additional hours pasr 29 hours

4) usual volume =   41200970

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