Rate Concept (Taps and Tanks)

First
Tap X flows at a rate of 2100 ml/min while Tap Y flows at a rate of 2500ml/min. Both taps were turned on at the same time to fill a tank with dimensions 50 cm x 40 cm x 30 cm. After 5 minutes, the plug at the bottom of the tank is removed, with the two taps still running. If the water is drained at a rate of 600 ml/min, what is the water level 2 minutes after the plug is removed?
(Ans: 15.5cm)

Filling Tap X (Rate) = 2100 ml/min
Filling Tap Y (Rate) = 2500 ml/min
Draining Plug (Rate) = 600 ml/min

(First 5 minutes)
Tap X + Tap Y (Rate) = 2100 + 2500 = 4600 ml/min
Volume of Water = 4600 ml/min x 5 min = 23 000 ml

(2 minutes after first 5 minutes)
Tap X + Tap Y - Plug (Rate) = 4600 - 600 = 4000 ml/min
Volume of Water = 4000 ml/min x 2 minutes = 8000 ml 

Total Volume of Water = 23 000 ml + 8000 ml = 31 000 ml
Water Level (Height) = Volume / Length / Breadth 

= 31 000 / 50 / 40 = 15.5cm


Second
At 9am, Mr Fernandez used 2 taps to fill up a tank. The first tap could fill the tank in 4 hours. The second tap could fill the tank in 3 hours. An hour after both taps were turned on, the second tap were faulty and stopped working. Mr Fernandez accidentally opened the 3rd tap which could drain a full tank completely in 2 hours. Instead of being filled, the tank was being emptied. How long did it take for the tank to be completely empty ?


1st Filling Tap (Rate) = 1/4 tank/hour
2nd Filling Tap (Rate) = 1/3 tank/hour
3rd Draining Tap (Rate) = 1/2 tank/hour

(1st Hour: 9am - 10am) (1st and + 2nd Filling Tap)
1st + 2nd Filling Tap (Rate) = 1/4 + 1/3 = 7/12 tank/hour
Amount of Tank = 7/12 tank/hour x 1 hour = 7/12 tank


(After 1st Hour) (1st Filling Tap - 3rd Draining Tap)
3rd - 1st Tap (Rate) = 1/2 - 1/4 = 1/4 tank/hour
Remaining Amount of Tank = 1 tank - 7/12 tank = 5/12 tank

Drainage (Time) = (5/12 tank) / (1/4 tank/hour) = 1 2/3 hour = 1 hour 40 minutes