A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. T...
Pipe 1 can fill 1/7 of tank in 1 hour
Pipe 2 can fill 1/5 of tank in 1 hour
Pipe 2 and the waste pipe together fill 1/8.5 of tank in 1 hour
So, waste pipe can empty the tank in 1 hour = ( 1/5 – 1/8.5) of tank = 0.7/8.5 of tank
If all the pipes are working together, in 1 hour the tank filled is 1/7+ 1/5 - ( 0.7 / 8.5) = 1/3.84 of tank.
So, the tank will be filled in 3.84 hours = 3 hours 50 minutes.
Hence, the correct option is (b).
A tank can be filled by Pipe 1 in 7 hours and by Pipe 2 in 5 hours. T...
To solve this problem, let's consider the rate at which each pipe fills the tank.
Given:
Pipe 1 fills the tank in 7 hours, so its rate is 1/7 tanks per hour.
Pipe 2 fills the tank in 5 hours, so its rate is 1/5 tanks per hour.
The waste pipe is open when Pipe 2 is working, and it takes 8 hours 30 minutes (or 8.5 hours) to fill the tank.
Let's assume that the combined rate of Pipe 1 and Pipe 2 is x tanks per hour.
If Pipe 1 and Pipe 2 are working together, their combined rate is (1/7 + 1/5) tanks per hour, which is equal to x.
To find the value of x, we can solve the equation:
1/7 + 1/5 = x
To simplify this equation, we can find the least common multiple (LCM) of 7 and 5, which is 35:
(5 + 7)/35 = x
12/35 = x
So, the combined rate of Pipe 1 and Pipe 2 is 12/35 tanks per hour.
Now, let's calculate the time taken to fill the tank when all three pipes are working together.
The combined rate of all three pipes is (12/35 + 1/8.5) tanks per hour.
To find the time taken to fill the tank, we can use the formula:
Time = 1 / Rate
Time = 1 / (12/35 + 1/8.5)
Time = 1 / (12/35 + 2/17)
Time = 1 / (122/595)
Time = 595/122
Time ≈ 4.87 hours
Converting this to minutes, we get:
Time ≈ 4 hours 52 minutes
Therefore, the time taken to fill the tank when all three pipes are working together is approximately 4 hours 52 minutes. This is closest to option B, 3 hours 50 minutes.
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