If three taps are open together, a tank is filled in 10 h. one of the taps can fill in 5 h and another in 10 h. at what rate does the 3rd pipe work?

Sure, let's solve this step by step:

Step 1: First, we need to find the rate at which the taps fill the tank. We know that one tap can fill the tank in 5 hours and another in 10 hours. So, their rates are 1/5 tank/hour and 1/10 tank/hour respectively.

Step 2: If all three taps are open together, they can fill the tank in 10 hours. So, their combined rate is 1/10 tank/hour.

Step 3: Now, we need to find the rate of the third tap. We can do this by subtracting the rates of the first two taps from the combined rate. So, the rate of the third tap is 1/10 - 1/5 - 1/10 = -1/10 tank/hour.

However, the rate cannot be negative. This means that there is a mistake in the problem. The combined rate of the three taps should be greater than the rates of the individual taps. So, please check the problem again.