Numerical answer
Pipes A and B can fill an empty tank in 20 hours and 30 hours respectively, and an outlet pipe C can empty the full tank in 15 hours. All three pipes are opened together at 9 a.m. on an empty tank, and C is closed at 11 a.m. After how many hours from 9 a.m. will the tank be full?
Show answer and solution
Answer: 13.6
Take the tank = 60 units. A fills 3 units/h, B fills 2 units/h and C empties 4 units/h.
From 9 to 11 a.m. (2 h) the net rate is 3 + 2 − 4 = 1 unit/h, so 2 units are filled.
Remaining = 58 units at 5 units/h (A + B) = 11.6 h.
Total time from 9 a.m. = 2 + 11.6 = 13.6 hours (the tank is full at 10:36 p.m.).
Tip: using LCM units avoids working with fractions.
From 9 to 11 a.m. (2 h) the net rate is 3 + 2 − 4 = 1 unit/h, so 2 units are filled.
Remaining = 58 units at 5 units/h (A + B) = 11.6 h.
Total time from 9 a.m. = 2 + 11.6 = 13.6 hours (the tank is full at 10:36 p.m.).
Tip: using LCM units avoids working with fractions.
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