Pipes A, B, and C can fill a tank individually in 5 min, 10 min, and 15 min respectively. Find the time taken to fill the tank when all three Pipes are opened simultaneously.
Question
Pipes A, B, and C can fill a tank individually in 5 min, 10 min, and 15 min respectively. Find the time taken to fill the tank when all three Pipes are opened simultaneously.
Solution
Step 1: Find the rate at which each pipe can fill the tank.
Pipe A can fill the tank in 5 minutes, so its rate is 1 tank/5 minutes = 0.2 tanks/minute. Pipe B can fill the tank in 10 minutes, so its rate is 1 tank/10 minutes = 0.1 tanks/minute. Pipe C can fill the tank in 15 minutes, so its rate is 1 tank/15 minutes = 0.067 tanks/minute.
Step 2: Add the rates together to find the combined rate.
The combined rate of all three pipes is 0.2 tanks/minute + 0.1 tanks/minute + 0.067 tanks/minute = 0.367 tanks/minute.
Step 3: Find the time it takes for all three pipes to fill the tank.
The time it takes for all three pipes to fill the tank is 1 tank / 0.367 tanks/minute = 2.72 minutes.
So, it will take approximately 2.72 minutes to fill the tank when all three pipes are opened simultaneously.
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