Answer:
x = 16.6666666667
Step-by-step explanation:
24x4 - 18x3 + 4x2 - 3x =0
24x4 = 96
18 x 3 = 54
4x2 = 8
96-54+8= 50
50/3 = 16.6666666667
Lets say, for ease, that the vat can hold a total of 70 gallons (or whatever you would like to use.) Use whatever number you want, I just picked this because it gives us a lot of clean numbers.
Now, if the inlet can fill it in 7 hours, that means that it is adding 10 gallons per hour. (70 gal/7 hours = 10 gal/hr)
For the outlet, use the same process, and you find that it drains the vat at 7 gallons per hour.
So, if you subtract the outlet from the inlet, you get 10 - 7 = 3 gallons per hour added.
Now just divide the size of the vat by that number, and you find your answer.
70 gallons / 3 gallons per hour = 23 1/3 hours.
