Math question. Please help :( I need exact answer and solution. Thank you!!! (Pipes)
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Math question. Please help :( I need exact answer and solution. Thank you!!! (Pipes)

[From: ] [author: ] [Date: 12-02-21] [Hit: ]
part of tank empty = 2/3 x cu.this empty part of tank was filled by pipe A alone in =30-5 = 25 hours.so, time taken by A alone to fill the entire tank = 25*3/2 hours.= 37.5 hours.......
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

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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.

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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

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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.

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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.

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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?
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