Bath Emptying Quiz Puzzle

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?