Three pipes can fill a tank in 6, 10, 15 hours respectively. If they are opened together, how long does it take to fill the tank?
Question
Three pipes can fill a tank in 6, 10, 15 hours respectively. If they are opened together, how long does it take to fill the tank?
Solution
To solve this problem, we first need to find the rate at which each pipe can fill the tank.
- The first pipe can fill the tank in 6 hours, so its rate is 1/6 of the tank per hour.
- The second pipe can fill the tank in 10 hours, so its rate is 1/10 of the tank per hour.
- The third pipe can fill the tank in 15 hours, so its rate is 1/15 of the tank per hour.
When all three pipes are opened together, their rates are added. So, the combined rate is 1/6 + 1/10 + 1/15 = 15/90 + 9/90 + 6/90 = 30/90 = 1/3 of the tank per hour.
Therefore, it will take 3 hours to fill the tank when all three pipes are opened together.
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