Another question justification a short solution but hard of do

 Is type is hard but is already end? To the question:

A water pump fills a reservoir in 4 hours and another pump takes 8 hours to fill the same reservoir. In how many minutes will the two pumps together fill the reservoir?

A) 160 minutes.

B) 120 minutes.

C) 340 minutes.

D) 456 minutes.

E) 234 minutes.

Justification, let's went to phylosophie and is that we have to tanks one in Germany with 80liters of capacity and other in USA with 120liters of capacity, and there in Germany but the pumps in Germany fill in 4 hours and 8 hours the tank, and in the USA other 2 pumps fill the tank also in 4 hours and 8 hours and the capacity is completely diferent, when I resolve that for the 1st time I explain for the professor that the capacity or volumen of the tank was irrelevant, and could be solved using the flow, my brain is type simplify, I think that solution of the site is a old one of the USA, is right but was a genius of USA, of so famous is very laborious, and my solution is more easy, so the Ameraaican was considered a genius because he solved so to the philosophy...

So where is irrelevant is the vazão - flow that is the velocity that is the volum of water by time, when you have a machine that counts in the instantaly you make pratically an vertical incision in the pipe, and had a disk that can measure the quantity of water passed by the disk in that 1-1second becuase is instantanly after sometime I gonna explain the instantaly velocity is the velocimeter of the car.

Now that you know what is flow the represetaion:

in Phisics if two grandities had the same letter, type velocity and volume, velocity is liter/minutes and volume is liters, the more complex is the velocity so the letter is capital "V", and the volume is small "v".

When we are calculating the same grandities but of diferent things, the grandity would represent with a very small letter of the thing like that pump A and pump B is VA and VB .

But also we can use for grandities that had the same first letter an diferent letter, so I gonna use that method.

I can use a letter for volume of the tang like Q or use 80liters, small numbers is to make easier the calculations I gonna show the 2 to you see that all work and is alway a small calculation.

A draw to make you happy I did myself in the paint.

1st of resolution, the volume of tank is the Q - so the 1st formula is Velocity = volum/time:

VA = Q/4   ---> The velocity of the water entering in the tank for the 1st pump is the volum Q divided by the time 4 hours.

VB = Q/8   ---> The velocity of the water entering in the tank for the 2nd pump is volum Q divided by the time 8 hours.

The velocity that I want is of the 2 pumps working together filling the tank that I will call VAB, if I was writing I would draw a line in the top of the AB

In mathematical idealizations I could say to you that is a ideal pump that flows all that water is just some artificialism that we can use to create ideals situations

VAB to solve is very wordy so pay attention to it in 8 hours of course this isn't the time for the tank but for the velocity so I am calculating the velocity, see if I didn't explaim you would agree with me but you would not know what I did so the velocity of the 2 pumps is in 8 hours and not in one hour is:

in 8 hour the pump A gonna throw 2 times the tank and the pump B one time so gonna be 3 times the tank, if I didn't explain do you know what I gonna just do?

VAB = 2Q+Q/8   ---> VAB = 3Q/8 and know that I had the velocity of my ideal pump or the 2 pumps, let's solve it:

V = v/t   ---> 3Q/8 = Q/t  Velocity is 3Q/8 and the other side of equittity is volume of the tank over the time I had the velocity and the volum is Q I want to know the time, so multiplying crossed the two equititties we gonna have:

but 1st one simplfication we can cancel the Q : 3Q/8 = Q/t  t = 8H/3

Transforming that to minutes is hours becuase was the grandity of the begining the tanks are filled in hours so the result is in hours becuase I didn't change the grandity and I gonna do that and 8x60/3 = 160.

Finished_____________2nd way________________

volume I gonna give a volume becuase Isaid in Germany is 80liters an in USA is 1200liters so the volum is irrelevant before the end of the calculation it would be cancelled rip off of the the solution that is important because if isn't irrelevant the question was bad constructed and hadn't validy solution.

So the volum being 80l:

VA = 80/4   ---> VA = 20L/h.   Here in one hour was pumped 20 liters

VB = 80/8   --->VB = 10L/h    Here in one hour was pumped 10 liters

So the VAB = volume that is pumped in 1 that is ---> VAB = 10+20   ---> VAB = 30(L/h)

So velocity of VAB is 30 liters each hour in right hand of the equality is the volum of 80 over the time that what I want discover: VAB = volum/t ---> 30L/h = 80L/t ---> t = 8/3 hour we reach the same result and know only transform in minutes that is 160 minutes and is finished.

Solve the problem is very short long is do it justifying. And for sure the rationalization isn't easy but the calculation.

Rute Bezerra de Menezes Gondim