A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tankQuestion Description : 25 hrs20 hrs35 hrs45 hrs
Question
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tankQuestion Description : 25 hrs20 hrs35 hrs45 hrs
Solution
To solve this problem, we first need to understand the relationship between the pipes.
- Let's denote the rate at which pipe A fills the tank as 'a'.
- According to the problem, pipe B is twice as fast as A, so its rate is '2a'.
- Similarly, pipe C is twice as fast as B, so its rate is '2*2a = 4a'.
When all three pipes are open, they fill the tank in 5 hours. So, the combined rate of the three pipes is 1 tank/5 hours = 0.2 tanks/hour.
We can set up the equation: a + 2a + 4a = 0.2.
Solving this equation gives us 'a' = 0.2/7 = 0.02857 tanks/hour.
To find out how long pipe A alone would take to fill the tank, we divide the total volume of the tank (1 tank) by the rate of pipe A: 1/0.02857 = 35 hours.
So, pipe A alone will take 35 hours to fill the tank. The correct answer is 35 hours.
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