The flow rate of a coolant into a chemical reactor, RtR_tRt, is adjusted every minute such that the sequence of flow rates forms an arithmetic progression, where t t\,t is the time in minutes.
In the 4th minute, the flow rate is 40 L/min. The total volume of coolant delivered during the first 10 minutes is 325 L. Determine the initial flow rate, aaa, and the constant change in flow rate per minute, ddd.
A secondary auxiliary system has an initial flow rate of 6 L/min, which increases by 2 L/min each minute. The total volume delivered by this auxiliary system over n n\,n minutes is TnT_nTn. Find the value of n n\,n such that the total volume delivered by the primary system, SnS_nSn, is equal to TnT_nTn, where n>0n > 0n>0.
