Answer:6 hours and 31 minutes
Explanation:
Time taken = Total work / Rate of work
Let's assume that the capacity of the pond is C.
The rate of work of the first water tank is C/16, which means it can refill 1/16th of the pond in 1 hour.
Similarly, the rate of work of the second water tank is C/11, which means it can refill 1/11th of the pond in 1 hour.
When both tanks are working together, their rates of work add up, so the combined rate of work is:
(C/16) + (C/11)
To find the time taken to refill the pond when both tanks are working together, we can use the formula:
Time taken = Total work / Rate of work
Since the total work is to refill the entire pond, which has a capacity of C, we can substitute this value:
Time taken = C / [(C/16) + (C/11)]
Now we can simplify the expression by finding the common denominator:
Time taken = C / [(11C + 16C) / (16 x 11)]
Time taken = C / (27C / 176)
Time taken = 176 / 27
Time taken = 6.5185 hours (rounded to four decimal places)
Therefore, it will take approximately 6.5185 hours, or 6 hours and 31 minutes, to refill the drained pond if both water tanks are working at the same time.