Problema Solution
at noon a pump started emptying a oil storage tank at a constant rate. at 2pm there were 1680 barrels left in the tank. at 5pm there were 600 barrels of oil remaining in the tank. write the particular equation for this function.
Answer provided by our tutors
let 'v' be the rate of pumping in barrels per hour
since in 3 hour (the time between 2 pm and 5 pm) the pump pumped 1680 - 600 = 1080 barrels of oil we can find the rate
v = 1080/3 = 360 barrels per hour
in 2 hours the pump will pump 2*360 = 720 barrels and there will be 1680 barrels left in the tank thus at the beginning the tank has
720 + 1680 = 2400 barrels of oil
now we can write the function
at noon t = 0, f(0) = 2400 - 0 = 2400 nothing has been pumped and the tank is full
at 2 pm (in 2 hours) f(2) = 2400 - 2*360 = 1680 barrels left in the tank
at 5 pm (5 hours since the start) f(5) = 2400 - 5*360 = 600 barrels left in the tank
the equation that describes the pumping is:
f(x) = 2400 - x*360, where x is the working time of the pump.