A pipe can fill a tank in 3 hours. There are two outlet pipes from the tank which can empty it in 7 and 10 hours respectively. If all the three pipes are opened simultaneously, then the tank will be filled in Question Description : 8 hours10 hours 11 hours9 hours
Question
A pipe can fill a tank in 3 hours. There are two outlet pipes from the tank which can empty it in 7 and 10 hours respectively. If all the three pipes are opened simultaneously, then the tank will be filled in Question Description : 8 hours10 hours 11 hours9 hours
Solution
To solve this problem, we first need to find the rate at which each pipe can fill or empty the tank.
- The first pipe can fill the tank in 3 hours, so its rate is 1/3 of the tank per hour.
- The second pipe can empty the tank in 7 hours, so its rate is -1/7 of the tank per hour (negative because it's emptying the tank).
- The third pipe can empty the tank in 10 hours, so its rate is -1/10 of the tank per hour.
If all three pipes are opened simultaneously, their rates will add up. So, the combined rate of the three pipes is (1/3 - 1/7 - 1/10) = 70/210 - 30/210 - 21/210 = 19/210 of the tank per hour.
To find out how long it will take to fill the tank at this combined rate, we divide the total volume of the tank (1) by the combined rate: 1 / (19/210) = 210/19 hours.
Therefore, if all three pipes are opened simultaneously, the tank will be filled in approximately 11 hours.
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