A tank fitted with two pipes is to filled with water. One pipe can fill it in 5 hours. After it has been open for 3 hours, the second pipe is opened and the tank is filled in 4 hours more. How long it would take the second pipe alone to fill the tank?
To solve this problem, we will break it down into smaller steps.
Step 1: Find the rate of filling of the first pipe per hour.
- Let's assume that the first pipe can fill the tank in 5 hours. So, in 1 hour, it fills 1/5th of the tank.
- Therefore, the rate of filling of the first pipe per hour is 1/5th of the tank.
Step 2: Determine the progress made by the first pipe in 3 hours.
- If the first pipe fills the tank at a rate of 1/5th of the tank per hour, in 3 hours it will fill (1/5) * 3 = 3/5th of the tank.
Step 3: Calculate the remaining volume of the tank after 3 hours.
- Since the first pipe filled 3/5th of the tank in 3 hours, the remaining volume of the tank is 1 - 3/5 = 2/5th of the tank.
Step 4: Find the rate of filling of both pipes together per hour.
- We know that both pipes working together can fill the remaining 2/5th of the tank in 4 hours.
- Therefore, the rate of filling of both pipes combined per hour is (2/5) / 4 = 1/10th of the tank.
Step 5: Calculate the time required for the second pipe to fill the remaining tank alone.
- Since both pipes together fill the tank at a rate of 1/10th per hour, the second pipe alone will fill at a rate of 1/10th - 1/5th = -1/10th per hour.
- To fill 2/5th of the tank, the second pipe will take (2/5) / (-1/10) = -4 hours.
- However, since time cannot be negative, we take the absolute value of -4, which is 4 hours.
Therefore, it would take the second pipe alone to fill the tank in 4 hours.
let the tank contain V units of volume
rate of first pipe = V/5 units/hr
rate of 2nd pipe = V/x units/hr
So the first pipe runs for 3 hrs
Volume = 3(V/5) = 3V/5
the second pipe runs for 4 hrs.
Volume filled by 2nd pipe = 4(V/x) = 4V/x
3V/5 + 4V/x = V
multiply by 5x
3Vx + 20V = 5xV
3x + 20 = 5x
x = 10
It would take 10 hrs using the 2nd pipe alone