A 600L water tank is full to the top. One day, it started leaking at a rate of 15L per hour, when it was half way, water is added at a rate of 20L per hour, how long will it take for the tank to be full again?

time to drain halfway: 300/15 = 20 hr

time to fill back up: 300/5 = 60 hr

Thanks for your response, but according to my teacher it's 80 hours. Could you please see why that is the answer.

well, 20+60=80

I guess she started counting when the tank started to leak...

To solve this problem, we need to determine the time it takes for the tank to be filled again.

Let's break down the problem into smaller steps:

Step 1: Find the total amount of water that leaks when the tank is half full.
Since the tank started leaking when it was full and leaks at a rate of 15L per hour, it takes (600L/2) / 15L/hour = 20 hours for the water level to reach halfway.

Step 2: Determine how much water has leaked at the halfway point.
We already found that it takes 20 hours for the tank to be half full. Therefore, the amount of water leaked in 20 hours is 15L/hour x 20 hours = 300L.

Step 3: Calculate the amount of water needed to fill the tank from halfway.
The tank needs to be filled with 600L of water, but since it is already halfway full (300L remaining), only 600L - 300L = 300L of water is needed to fill the tank completely.

Step 4: Calculate the time it takes to fill the remaining 300L.
Water is being added to the tank at a rate of 20L per hour. Therefore, it takes 300L / 20L/hour = 15 hours to fill the remaining 300L.

Step 5: Find the total time it takes to fill the tank again.
To find the total time to fill the tank again, we sum the time it took for the tank to be half full (20 hours) and the time it took to fill the remaining 300L (15 hours). Therefore, it takes 20 hours + 15 hours = 35 hours to fill the tank completely.

So, it will take 35 hours for the tank to be full again.