calculus homework

Question

A village wishes to measure the quantity of water that is piped to a factory during a typical morning. A gauge on the water line gives the flow rate (in cubic meters per hour) at any instant. The flow rate is about 100m3/hr at 6 am and increases steadily to about 280m3/hr at 9 am. Using only this information, give your best estimate of the total volume of water used by the factory between 6 am and 9 am.

Answer 1

Call  6 am   t=0,  then 9 am corresponds to t = 3

 

A straight line estimate of the rate as a function of t is:

 

  R(t) = 100 + 60 t.

 

The volume if the water piped is the integral of R over t   with the limits:   0 and 3

 

  V =  100 t + 30 t²  |₀³   =  570  m³ 

 

 

The same result can be obtained by figuring the average flow rate (190 ) and multiplying by 3