Respuesta :
Answer with explanation:
It is gven that, Three taps A, B and C are emptying the tank.
Time taken by Tap A to empty the tank completely =17.0 Hours
Time taken by Tap B to empty the tank completely =6.8 Hours
Time taken by Tap C to empty the tank completely =5.2 Hours
Time taken by three taps, A , B and C together to empty the tank completely
[tex]=\frac{1}{17}+\frac{1}{6.8}+\frac{1}{5.2}\\\\=\frac{14}{68}+\frac{10}{52}\\\\=\frac{88}{221}[/tex]
Let V be the volume of water in the tank.
→Volume of water in the tank after half an hour when the tap C has been blocked
[tex]=\frac{88}{221} \times \frac{30}{60}\\\\=\frac{44V}{221}[/tex]
→→% of Volume of water in the tank after half an hour, when the tap C has been blocked
[tex]=\frac{44V}{221V}\times 100\\\\=19.9095[/tex]
=19.91%
Let Time taken by the taps to empty the tank =t hours
When volume of water out of the tank is equal to volume of water inside the tank , the tank is said to be emptied.
[tex]\rightarrow \frac{88V}{221}\times t=V\\\\t=\frac{221}{88}\\\\t=2.52 \text{Hours}[/tex]
=2.52 hours (Approx)
