One pipe can fill a cistern in 1.5 hours while a second pipe can fill it in 2 and 1/3 hours.Three pipes working together fill the cistern in 42 minutes.How long would it take the third pipe alone to fill the tank?
using minutes for all pipes, we have
1/90 + 1/140 + 1/x = 1/42
x = 180
so, it will take the 3rd pipe 3 hours
rate for pipe 1 --- 1/(3/2) = 2/3
rate for pipe 2 --- 1/(7/3) = 3/7
rate for pipe 3 --- 1/x
combined rate = 2/3 + 3/7 + 1/x
= (14x + 9x + 21)/(21x) = 42/60 = 7/10
1/[ (14x + 9x + 21)/(21x) ] = 42/60 = 7/10
21x/(23+21) = 7/10
210x = 161x + 147
x = 147/49
= 3 hours
To find out how long it would take the third pipe alone to fill the tank, we can calculate their individual rates of filling the tank.
Let's start by finding the rate at which the first pipe fills the cistern. We know that it takes 1.5 hours for the first pipe to fill the cistern, so its rate of filling would be 1 cistern per 1.5 hours, or 1/1.5 cisterns per hour.
Similarly, the second pipe takes 2 and 1/3 hours to fill the cistern. Converting this to a mixed fraction, we get 2 + 1/3 = 6/3 + 1/3 = 7/3 hours. Therefore, the rate at which the second pipe fills the cistern is 1 cistern per 7/3 hours, or 3/7 cisterns per hour.
Now, let's consider the combined rate at which all three pipes fill the cistern. We are given that, when working together, they can fill the cistern in 42 minutes. Since there are 60 minutes in an hour, this is equivalent to 42/60 = 7/10 hours. Therefore, the combined rate at which the three pipes fill the cistern is 1 cistern per 7/10 hours, or 10/7 cisterns per hour.
To find the individual rate at which the third pipe fills the cistern, we subtract the combined rate of the first two pipes (1/1.5 + 3/7 = 7/10) from the combined rate of all three pipes (10/7). Therefore, the rate at which the third pipe fills the cistern is (10/7) - (7/10) = (100/70) - (49/70) = 51/70 cisterns per hour.
Finally, to determine how long it would take the third pipe alone to fill the cistern, we take the reciprocal of its rate. Therefore, it would take the third pipe 70/51 hours to fill the tank.
In minutes, this is equal to (70/51) * 60 = 82.35 minutes (approximately).
So, it would take the third pipe alone approximately 82.35 minutes to fill the tank.