A tank is being filled with water using a pump that is old and slows down as it runs. The table below gives the rate at which the pump pumps at
ten-minute intervals. If the tank is initially empty, approximate how much water is
in the tank after 90 minutes?
Elapsed time
(Minutes) 0 10 20 30 40 50 60 70 80 90
Rate
(gallons / minute) 42 40 38 35 35 32 28 20 19 10

Question

A tank is being filled with water using a pump that is old and slows down as it runs. The table below gives the rate at which the pump pumps at 
ten-minute intervals. If the tank is initially empty, approximate how much water is 
in the tank after 90 minutes? 
Elapsed time 
(Minutes) 0 10 20 30 40 50 60 70 80 90 
Rate 
(gallons / minute) 42 40 38 35 35 32 28 20 19 10

anonymous · Answer

The approximation depends on what kind of approximating technique you'd like to use... You can determine the amount of water at 90 minutes with a Riemann sum, but there are a few different setups we can consider (in increasing order of accuracy: upper/lower rectangular, trapezoidal, polynomial interpolation, etc)