Water flows into a tank according to the rate F (t) = (6+t) / (1+t), and at the same time empties out at the rate E (t) = ln (t+2) / (t+1), with both F (t) and E (t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 minutes.

Question

Mathematics

Frankie

5 May, 03:32

Water flows into a tank according to the rate F (t) = (6+t) / (1+t), and at the same time empties out at the rate E (t) = ln (t+2) / (t+1), with both F (t) and E (t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 minutes.

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Serena Bullock · Answer 1

F (t) = 1.5 gallon / min

E (t) = 5.5 gallon/min

Step-by-step explanation:

The rate at which water flows into the tank = F (t)

The rate at which water is emptied from the tank = E (t)

F (t) = (6+t) / (1+t)

E (t) = ln (t+2) / (t+1)

When t = 10 mins

F (t) = (6 + 10) / (1+10)

= 16/11

F (t) = 1.5 gallon / min

E (t) = ln (10 + 2) (10+1)

= ln (12) (20)

= ln (240)

E (t) = 5.5 gallon/min