tap a can fill a tank in 10 min and tap 2 in 15 min .if both the taps are opened and after 2min of tap 1 is closed then time taken by tap 2 to fill the tank
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Answers
Answer:
Work = Rate*Time
Tap A takes 2 minutes to fill tank, so Tap A’s rate is Work/Time =1/2 tank per minute
Tap B takes p minutes to fill tank, so Tap B’s rate is Work/Time =1/p tank per minute
Since Taps A and B together take more than 2 minutes to fill, Tap B is obviously draining while Tap A is filling.
Together, Work = (Ra + Rb)(2+2/3) minutes.
Plugging in the numbers, Work = (1/2+1/p)*8/3, so that 3/8 = (1/2+ 1/p)
Then 3/8 = 4/8+1/p and subtracting 4/8 from both sides,
-1/8= 1/p = Tap B’s Rate
Then, to empty, -Work = (-1/8)*Time, so Time = 8 minutes,
And Tap B takes 8 minutes to empty the tank.
As a check on this, their combined rates are 1/2-1/8, or 3/8
So what happens in 8 minutes? Work = R*T = 3/8*8 = 3 fills
And in 8 minutes, you would expect the A Tap to fill the tank 4 times, while the B Tap empties it once, making for 3 complete fills.
Answer:
Noticed that Tap A alone can fill the tank in just 2 minutes and together with Tap B, they took more than Tap A's speed.
Looks like Tap B is not designed to fill the tank but rather to drain or to empty it.
1A=12" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1A=121A=12
1B=1p" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1B=1p1B=1p
12+1p=183" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">12+1p=18312+1p=183
1p=183−12" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1p=183−121p=183−12
1p=38−12" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1p=38−121p=38−12
1p=3–48=(−18)" role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">1p=3–48=(−18)1p=3–48=(−18)
p=−8 minutes." role="presentation" style="display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">p=−8 minutes.p=−8 minutes.
-8 minutes to fill the tank (I'm not sure if there's such a term), or..
8 minutes to drain
Assuming Tap A will automatically stop upon sensing that the tank is already full after 2 2/3 mins, Tap B can empty the tank in the next 8 minutes.
how long does it take Tap B to empty the tank?
Adding the first 2 2/3 minutes to Tap B's draining speed of 8 mins, without any interruption, total time would be 10 and 2/3 minutes..
Tap A = 1/2 = 100% per 2 min = 50% per min
Tap B = -1/8 = -100% per 8 min= -12.5% per min
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