Amount

[Guest]

A milk delivery person has two sixteen gallon containers of milk. His customers are on four different streets. He delivers the same number of quarts on each street. After each street he dilutes the milk with water until the containers are full again. After all deliveries, forty quarts and one pint of pure milk remained in the containers. Calculate amount of pure milk delivered on each street. Thanks.

[Guest]

Is the milk diluted evenly throughout all the ciustomers..??
If the containers are full of pure milk to start with does that mean the first street gets pure milk.
Dilution only starts after the first street has been delivered.
Also how does he know he has 40 quarts and one pint left if it is diluted with water.
So does the last street get puer milk as well..??
Is anybody complaining about getting very "watery" milk...??

[Guest]

Each customer received one quart.
After the first street dilution starts.
The problem asks how much pure milk was delivered on each street- ( I don't understand how after dilution).
I don't understand how pure milk remained.
The problem states "all his happy customers".

Answer given shows an amount of pure milk delivered on each street- No solution given. I am interested in the solution.

Thanks.

[Guest]

Well then, in the absence of adequate information being given, we will assume the containers are full at the start with pure milk. The milkman delivers pure milk to his customers on the first street. At the end of the first street he fills the partly empty containers with water and mixes it as evenly as possible, and then delivers to customers in the second street ( not pure milk but a mix of water and milk), at the end of the second street he refills the containers and mixes with what is left and delivers same for third street, then refills and mixes and delivers to 4th street. He is then left with a mixture of water and milk which if we know the mix ratio ( say 50% water) then we can work out how much pure milk is in it. Similary some of the customers may get 50% water so that is equivilant to getting 50% of pure milk.

The question says the containers (meaning both) are filled with water at the end of each street so the milkman cannot keep one for pure milk and mix in the other. Only 2 containers are mentioned and both are filled with water at the end of each street. Also both sixteen gallon containers are full at the start so no room for dilution at the start for the first street
Question says he has 2 sixteen gallon containers of milk.

If no more information is forthcoming we will provide a solution on that basis.

[Guest]

That is all the information. Thanks.

[Guest]

Nobody must be going to even attempt this question........

If we work in pints all units will be same.

At start 2 x 16 gallons = 256 pints

At end 40 quarts plus 1 pint = 81 pints

Street 1 gets full 100% milk.....no dilution.

Let us imagine the milk container is divided into P parts and as the amount delivered to each street then 1/P x 256 pints of liquid is delivered. The

containers are filled each time and each street gets the same quantity mixed or not mixed. So then the amount delivered to each street equals the amount of

water added at end on each street.

At end of Street 1 milk is poured from one container to the other to even the levela and the same amount of water is added to each to fill the containers and

keep the concentrations the same in each container.

There will now be 1/P x 256 water and (P-1)/P x 256 milk in the containers. Diluted with the water.

Next 1/P x 256 pints of this mix will be delivered to street 2. Then the containers evened up and filled again and so on

Street 3 will then get a mixture 1/P x 256 of mix already diluted and will only contain (P-1)/P concentration of milk.

So Street 3 gets a dilution ((P-1)/P)^2

and Street 4 gets ((P-1)/P)^3

Water is again added at end of Street 4 and the concentration is now.....((P-1)/P)^4 milk.

We are told this contains 81 pints of milk. That means 81 pints of milk to 256 pints of milk = 81/256

So...... (((P-1)/P)^4) = (81/256)

and the numbers are easy......(((P-1)/P)^4) = ((3^4 / (4^4))

So take 4th root of both sides .... (P-1)/P = 3/4.......3P = 4P-4.....P = 4

So number of parts is 4......delivery is 1/4 x 256 of liquid to each street....and 3/4 x 256 will be diluted with 1/4 x 256 water for the next street.

So Street 1 gets 1/4 x 256 pure milk = 64 pints

Street 2 gets 1/4 x 256 x 3/4 = 48 pints pure milk mixed with 16 pints of water.

Street 3 gets 1/4 x 256 x 9/16 = 36 pints pure milk mixed with 28 pints of water.

Street 4 gets 1/4 x 256 x 27/64 = 27 pints pure milk mixed with 37 pints water.

and after filling again what is left is 81/256 x 256 = 81 pints pure milk mixed with 111 pints of water that was already mixed plus the 64 pints added giving 175 pints water no in the combined containers 256 pints total.

3/4 squared is 9/19
3/4 cubed is 27/64
3/4 to 4th power is 81/256


...................Simple...............