The hot tap water fills the bathtub in 10 minutes, the cold tap water in 5 minutes, and the drain empties it in 20 minutes. How much time does it take to fill the bathtub
by 
bertrand017
ANSWERS: 2
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15 min.?
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Reformulation: - if the drain and the cold tap are closed, the hot tap water fills the bathtub in 10 minutes, - if the drain and the hot tap are closed, the cold tap water fills the bathtub in 5 minutes, - if the cold tap and the hot tap are closed, the drain empties the full bathtub in 20 minutes. The filling velocities are (negative filling = emptying): hot tap: 1 bathtub/10 mn = 1/10 bathtub/mn cold tap: 1 bathtub/5 mn = 1/5 bathtub/mn drain: -1 bathtub/20 mn = - 1/20 bathtub/mn If everything is working at once, the total velocity is: (1/10 + 1/5 - 1/20) bathtub/mn = (2/20 + 4/20 - 1/20) bathtub/mn = (5/20) bathtub/mn = (1/4) bathtub/mn Under those conditions, the bathtub will fill in 4 minutes.
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