Pipe A and Pipe B could fill the tank in 15h if they both opened. One day, after the two pipes were opened for 5h, pipe B was closed, and pipe A tank alone in 30h. How many hours will it take for pipe A to fill the tank alone?
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Pipe A and Pipe B could fill the tank in 15 h if they both opened → you divide by 3
→ Pipe A and Pipe B could fill (1/3) of the tank in 5 h if they both opened.
→ So pipe A (after pipe B was closed) can fill (2/3) of the tank in 30 h.
If pipe A (alone) can fill (2/3) of the tank in 30 h → you multiply by 3/2
→ it means that the pipe A can be able to fill (2/3) * (3/2) of the tank in : 30 h * (3/2)
→ the pipe A (alone) can be able to fill the tank in : 45 h
→ Pipe A and Pipe B could fill (1/3) of the tank in 5 h if they both opened.
→ So pipe A (after pipe B was closed) can fill (2/3) of the tank in 30 h.
If pipe A (alone) can fill (2/3) of the tank in 30 h → you multiply by 3/2
→ it means that the pipe A can be able to fill (2/3) * (3/2) of the tank in : 30 h * (3/2)
→ the pipe A (alone) can be able to fill the tank in : 45 h
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let volume of the tank = x cu. l
in 15 hours together they fill the tank totally [i.e. x cu. l]
on the day when 2 pipes were both open for 5 hrs, quantity of tank that would've been filled = x/3 cu. l
so, part of tank empty = 2/3 x cu. l
this empty part of tank was filled by pipe A alone in =30-5 = 25 hours.
it means that time taken by A to fill 2/3 x [2/3 part of total volume] = 25 hours
so, time taken by A alone to fill the entire tank = 25*3/2 hours.
= 37.5 hours.
in 15 hours together they fill the tank totally [i.e. x cu. l]
on the day when 2 pipes were both open for 5 hrs, quantity of tank that would've been filled = x/3 cu. l
so, part of tank empty = 2/3 x cu. l
this empty part of tank was filled by pipe A alone in =30-5 = 25 hours.
it means that time taken by A to fill 2/3 x [2/3 part of total volume] = 25 hours
so, time taken by A alone to fill the entire tank = 25*3/2 hours.
= 37.5 hours.
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Assuming 'pipe A tank alone in 30h' means that if pipe A was on its own from the start, it would take 30 hours:
Both pipes must be the same because when they are both open, it takes exactly half the time.
This means that when they are both open for 5 hours, the tank is exactly a third full, so 2/3 * 30 = 20h
Both pipes must be the same because when they are both open, it takes exactly half the time.
This means that when they are both open for 5 hours, the tank is exactly a third full, so 2/3 * 30 = 20h
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The rate of A +B = 1 tank/15 hours.
Therefore: 1tank/15 hours x 5 hours= 1/3 tank - Pipe B is switched off at this point.
Therefore A's rate= 2/3 tank/ 30 hours.
Therefore it takes A to fill a tank by itself
2/3 tankx 3/2/ 30hours x 3/2= 1 tank/45 hours.
A fills one tank in 45 hours.
Therefore: 1tank/15 hours x 5 hours= 1/3 tank - Pipe B is switched off at this point.
Therefore A's rate= 2/3 tank/ 30 hours.
Therefore it takes A to fill a tank by itself
2/3 tankx 3/2/ 30hours x 3/2= 1 tank/45 hours.
A fills one tank in 45 hours.
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15A + 15B = 1 tank filled and 35A + 5B= 1 tank filled
-3(35A + 5B = T)
-105A - 15B = -3T
15A + 15B = T
-90A = -2T
A = 1/45T so Pipe A fills 1/45 of the tank per hour
so it will take 45 hours for pipe A alone to fill the tank.
-3(35A + 5B = T)
-105A - 15B = -3T
15A + 15B = T
-90A = -2T
A = 1/45T so Pipe A fills 1/45 of the tank per hour
so it will take 45 hours for pipe A alone to fill the tank.
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When you say "pipe A tank alone in 30h" do you mean it took pipe A 30 MORE hours for a total of 35 hours or a total of 30 hours to include the first 5 hours?