Four years ago we published an interesting puzzle about filling a bath, which can be seen here. Here we have a similar puzzle but this time about emptying a bath - enjoy!
"Using the hot tap I can fill the bath in ten minutes . . ."
"Stop, I know this one."
"No you don't, and the cold tap fills it in four minutes . . ."
"Yes, yes. The hot tap fills one-tenth of the bath in a minute, the cold tap one-quarter, and together they fill seven-twentieths. So it takes two and six-sevenths minutes to fill the bath using both taps."
"You are wrong, because you didn't wait for me to say that the cold tap runs twice as fast as the hot tap . . ."
"Well, now you are wrong, because if that is the case the cold tap would fill the bath in five minutes not four!"
"You won't let me finish. This takes place with the plug out of the bath, so the hot tap has to cope with more leakage than the cold tap. And anyway, I don't want to know how long it takes to fill the bath - I want to know how long the bath will take to empty once it is full."
So, how long will the bath take to empty?
As the hot tap runs half as fast as the cold tap you would expect it to take eight minutes to fill the bath, but it takes ten. It takes an extra two minutes to cope with the extra six minutes of leakage.
On that basis it would take the hot tap ten minutes to put in enough water to drain through the plughole in 30 minutes.
So the bath would be empty 30 minutes after starting to fill it using the hot tap, that is 20 minutes after it is full - wherever the water came from.
The bath takes 20 minutes to empty.