Question

Three taps are emptying a tank Tap A can empty the full tank in 17.0 hours, tab B in 6.8 hours and tap C in 5.2 hours All taps are left open. But after 0.5 hours, tap C becomes blocked a) What PERCENTAGE of the tank has been emptied when C becomes blocked? remember to include a % s n , the answer 27 Percents 2 Marks How long does it take in total to empty the tank? ours 2 Marks

Answer 1

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

`=(1)/(17)+(1)/(6.8)+(1)/(5.2)\\\\=(14)/(68)+(10)/(52)\\\\=(88)/(221)`

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

`=(88)/(221) * (30)/(60)\\\\=(44V)/(221)`

→→% of Volume of water in the tank after half an hour, when the tap C has been blocked

`=(44V)/(221V)* 100\\\\=19.9095`

=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.

`\rightarrow (88V)/(221)* t=V\\\\t=(221)/(88)\\\\t=2.52 \text{Hours}`

=2.52 hours (Approx)