It takes one day to fill the vat
With this large pipe, two days with that;
The third pipe needs but one day more;
The fourth pipe fills the vat in four.
If all four pipes together run,
How long before the task is done?!
Happy birthday Cphill. But, I get a different answer!!.
The first, or large pipe, will fill 1/24 of the vat in 1 hour. The second will fill 1/48 of the vat in 1 hour. The third will fill 1/72 of the vat in 1 hour. And the fourth will fill 1/96 of the vat in 1 hour. Hence, all pipes together will fill: 1/24+1/48+1/72+1/96=25/288 of the vat in 1 hour. It, therefore, follows that altogether they will fill 1/288 of the vat in 1/25 of an hour, and the whole vat in 288/25 hours. Therefore, it will take the four pipes running at the same time: (288/25) / 24 =12/25 days, or just slightly under half a day.
+129840 Th first pipe fills the whole vat in one day
The second fills 1/2 the vat in one day
The third fills 1/3 of the vat in one day
And the fourth fills 1/4 of the vate in one day
To determine how long the pipes working together will take to fill the vat...take the reciprocal of
[1 + 1/2 + 1/3 + 1/4 ] = 25/12 → 12/25 days
Proof:
Sum ..... [ work done by each pipe in one day * no. of days working] = 1 [ the total job done]
1(12/25) + (1/2)(12/25) + (1/3)(12/25) + (1/4) (12/25) = 1
Happy birthday Cphill. But, I get a different answer!!.
The first, or large pipe, will fill 1/24 of the vat in 1 hour. The second will fill 1/48 of the vat in 1 hour. The third will fill 1/72 of the vat in 1 hour. And the fourth will fill 1/96 of the vat in 1 hour. Hence, all pipes together will fill: 1/24+1/48+1/72+1/96=25/288 of the vat in 1 hour. It, therefore, follows that altogether they will fill 1/288 of the vat in 1/25 of an hour, and the whole vat in 288/25 hours. Therefore, it will take the four pipes running at the same time: (288/25) / 24 =12/25 days, or just slightly under half a day.
