Running a bath (quiz)

6 minutes

misterq wrote:

It takes one tap twelve minutes to run a bath, whilst it takes the other six minutes to fill it up. The plug has been left out how ever, and the bath will empty in eight minutes. If both taps are on full and the plug is left out, how long will it take for the bath to fill up, if it will fill up at all?

If it takes one tap 12 minutes and the other 6 minutes , the mean difference what it takes both taps is 9 minutes

If the bath empties in 8 minutes then the bath is filling up by ” 1 minutes worth ” of the 9 minutes it needs to fill up every 9 minutes. 9 x 9 = 81 to fill the bath logic would dictate

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lindaclemenza7

The first step is to establish the capacity of the bath when full, for this I will create a fictional unit known as bath units. Using the first tap as a reference, the flow rate is 1 bu/min. This gives the bath a capacity of 12 bu. The second tap is twice as fast, so has a flow rate of 2 bu/m.

Next we must establish the flow rate of the drain. If it empties 12 units in 8 minuites then the flow rate must be 1.5 bu/m (12/8).

Turning on both taps gives us antotal input flow of 3 bu/m and, and the output flow remains the same at 1.5 bu/m. Resulting in a net flow of 1.5 bu/m (3-1.5). So we know that the bath will fill eventually. To calculate the time we must divide the capacity of the bath by the net flow rate of the system (12/1.5).

This gives the fill time of the bath to be 8 minutes.

Edit:

To clarify, a bath unit (bu) is defined as how much water is produced by the first tap in one minuite.

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TheNorfolkMafia

draculina wrote:

The first step is to establish the capacity of the bath when full, for this I will create a fictional unit known as bath units. Using the first tap as a reference, the flow rate is 1 bu/min. This gives the bath a capacity of 12 bu. The second tap is twice as fast, so has a flow rate of 2 bu/m. Next we must establish the flow rate of the drain. If it empties 12 units in 8 minuites then the flow rate must be 1.5 bu/m (12/8). Turning on both taps gives us antotal input flow of 3 bu/m and, and the output flow remains the same at 1.5 bu/m. Resulting in a net flow of 1.5 bu/m (3-1.5). So we know that the bath will fill eventually. To calculate the time we must divide the capacity of the bath by the net flow rate of the system (12/1.5). This gives the fill time of the bath to be 8 minutes. Edit: To clarify, a bath unit (bu) is defined as how much water is produced by the first tap in one minuite.

You have redeemed yourself drac from the goat shame.. I knew you had it in you

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misterq