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A total of 7 inlet and outlet pipes are fitted to a tank. Each inlet pipe can fill the tank (when empty) in 24 hours. Each outlet pipe can empty the tank (when full) in 36 hours. If all the pipes are opened simultaneously, the tank which is initially empty will be filled in 12 hours. The number of inlet pipes fitted to the tank is _____.

Question

A total of 7 inlet and outlet pipes are fitted to a tank. Each inlet pipe can fill the tank (when empty) in 24 hours. Each outlet pipe can empty the tank (when full) in 36 hours. If all the pipes are opened simultaneously, the tank which is initially empty will be filled in 12 hours. The number of inlet pipes fitted to the tank is _____.

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Solution

Let's denote the number of inlet pipes as 'x' and the number of outlet pipes as '7 - x' (since the total number of pipes is 7).

  1. The rate at which each inlet pipe can fill the tank is 1/24 tank/hour. So, the rate at which all inlet pipes can fill the tank is x/24 tank/hour.

  2. The rate at which each outlet pipe can empty the tank is 1/36 tank/hour. So, the rate at which all outlet pipes can empty the tank is (7 - x)/36 tank/hour.

  3. If all the pipes are opened simultaneously, the tank is filled in 12 hours. This means that the net rate at which the tank is filled is 1/12 tank/hour.

Setting these rates equal to each other gives us the equation:

x/24 - (7 - x)/36 = 1/12

Solving this equation will give us the value of 'x', which is the number of inlet pipes.

Let's solve it:

First, find a common denominator for the fractions, which is 72 in this case. Multiply each term by 72 to get rid of the fractions:

3x - 2(7 - x) = 6

Simplify the equation:

3x - 14 + 2x = 6

Combine like terms:

5x - 14 = 6

Add 14 to both sides:

5x = 20

Finally, divide by 5:

x = 4

So, there are 4 inlet pipes fitted to the tank.

This problem has been solved

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