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Pipe X, Y and Z can fill a tank in 10 minutes, 5 minutes and 10 minutes respectively. Find the time taken by the tank to be filled, if all the pipes are opened simultaneously.

Question

Pipe X, Y and Z can fill a tank in 10 minutes, 5 minutes and 10 minutes respectively. Find the time taken by the tank to be filled, if all the pipes are opened simultaneously.

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Solution

Sure, let's solve this step by step:

Step 1: Find the rate at which each pipe can fill the tank. This is done by taking the reciprocal of the time it takes for each pipe to fill the tank individually.

  • Pipe X can fill the tank at a rate of 1/10 tanks per minute.
  • Pipe Y can fill the tank at a rate of 1/5 tanks per minute.
  • Pipe Z can fill the tank at a rate of 1/10 tanks per minute.

Step 2: Add up the rates to find the combined rate when all pipes are opened simultaneously.

  • Combined rate = (1/10) + (1/5) + (1/10) = 1/10 + 2/10 + 1/10 = 4/10 = 2/5 tanks per minute.

Step 3: Find the time it takes for the tank to be filled at the combined rate. This is done by taking the reciprocal of the combined rate.

  • Time = 1 / (2/5) = 5/2 = 2.5 minutes.

So, if all the pipes are opened simultaneously, the tank will be filled in 2.5 minutes.

This problem has been solved

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