The Mean Value Theorem

Water in a reservoir As a result of a heavy rain, the volume of water in a reservoir increased by 1400 acre-ft in 24 hours. Show that at some instant during that period the reservoir’s volume was increasing at a rate in excess of 225,000 gal/min. (An acre-foot 43,560 ft3is the volume that would cover 1 acre to the depth of 1 ft. A cubic foot holds 7.48 gal.)

Step 1 of 2</p>

In this problem we have to show that at some instant during that period the reservoir’s volume was increasing at a rate in excess of 225,000 gal/min.

Given that the volume of water in a reservoir increased by hours.

Step 2 of 3 </p>

Let volume of the water in the reservoir at time t.

And be the initial amount.

is the number of minutes passing from the beginning,

In hours we have

gallons be the amount of water contained in the reservoir after the rain.