If hot and cold water taps are turned on altogether, a bath is filled in three minutes but if the cold tap was only half opened it would take one minute forty eight seconds longer. How long would the hot tap alone take to fill the bath?

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  12 minutes

Step-by-step explanation:

Let c and h represent the filling times for the cold and hot taps, respectively. When the cold tap is 1/2 open, we presume that means the filling time becomes 2c.

In terms of baths per minute, the relationships are ...

  1/c + 1/h = 1/3

  1/(2c) +1/h = 1/(3 +1.8) . . . . . 1:48 min:sec is 1.8 minutes

Subtracting the first equation from twice the second, we get ...

  2(1/(2c) +1/h) -(1/c +1/h) = 2(1/4.8) -(1/3)

  1/h = 2/4.8 -1/3 = 1/12

  h = 12

It takes the hot tap 12 minutes to fill the tub alone.

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