A group of research laboratories share a deionized water system, which is monitored by engineers Bertha and Elias. The tank holds 14,500 gallons of water. The filling and consumption rates are 236 gal/hr and 181 gal/hr. One busy day before some important deadlines, the tank holds 41.2% of the maximum capacity when the consumption rate increases at 3.67t gal/hr, where t is time in hours. Assuming that the density of water is constant, calculate the following unknowns.
Volume of water in the tank at 23.6 hr =
Ex: 5,120 gal
Time when the tank would first become empty =
Ex: 54.6 hr
Maximum volume observed =
Ex: 5,680 gal