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Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?

Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there? 2.5 3 4 5 6

so in 1 hour we get 12 liters, 54 liters will take 54/12 =4.5 hours.

bu it takes 12 hours to fill up, which means 12-4.5hours=7.5hrs are due to big pipes

Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?

Water flows into an empty tank of 54 liters via 12 small pipes. The rate of each pipe is 1 liter per hour. However, water flows out of the tank via several big pipes at the rate of 1.5 liter per hour. If after 12 hours, the tank is completely full, how many big pipes are there?

If the tank fills up to 54L in 12 hours then it is keeping 4.5L per hour. If the small pipes are putting in 12L per hour that means that 12L - 4.5L = 7.5L being lost out of the big tank per hour. Loss of an individual big pipe per hour is 1.5L so take 7.5 / 1.5 and that gives you 5 big pipes.

Hopefully somebody knows to shut off the water or it's going to make a mess.

I am good with math... except word problems, I always have a hard time setting up the problem. In this particular case, (for my benefit) I drew a little picture that represents the tank, and then drew a line that assumed a rate of 12 liters per hour going in. Then because I started to panic, I just selected C at random and tried it. I found that after 12 hours, it would overflow at 72 liters. So I knew that more material had to exit the tank, meaning I would try adding a pipe. I tried answer D, plugged it in and it worked. Not sure if I was just lucky or what... I ultimately got to the answer, but I wish I knew how to set up the problem automatically like many people here in the forum.

Nice equation setup. I need to get better at this. I picked numbers to come up with the answer to this problem though and was lucky enough to hit D on the first try. _________________

I'm trying to not just answer the problem but to explain how I came up with my answer. If I am incorrect or you have a better method please PM me your thoughts. Thanks!

54 is the total ending volume. We know that inflows occur at a rate of 12 liters per hour (1 liter per hour for 12 small pipes). It says in the prompt that the entire tank is full after 12 hours. Therefore we can take 144 - 54 = 90 (90 is the amount that has flowed out of the tank in this 12 hour time). We then take 90/12 = 7.5 to find out 7.5 liters flows out per hour. Then 7.5/1/5 = 5. (total liters per hour divided by rate per large pipe to yield total number of large pipes).

inflow of water(12 hrs) = 12*12 = 144, But total water in the tank after 12 hrs = 54 Outflow of water (12 hrs) = (144-54) = 90/12 = 7.5 Outflow capacity = 1.5. So total number of outflow pipes = 7.5/1.5 = 5

In 12 hours, 12 pipes will fill the tank by 12*12 = 144 litres. But as the tank can only take 54 litres, 144 - 54 = 90 litres should be the outgoing water.

As 1.5 litre is the size of the outgoing tube, in 12 hours 90/(12*1.5) = 5 pipes will be used to drain out the excess water.