Final answer:
To fill a water reservoir in 4 hours instead of 10 hours using identical pumps, an additional 3 pumps would be required, as the calculation shows that 5 pumps are needed in total.
Step-by-step explanation:
The student's question "Two identical pumps fill up a water reservoir in 10 hours, how many additional pumps would it take for it to be filled up in 4 hours?" involves applying the concept of work rate from Mathematics. The problem can be approached by determining the rate at which one pump can fill the reservoir, and then figuring out how many identical pumps would be needed to fill the reservoir in the shorter time frame of 4 hours. Since two pumps work together to fill the reservoir in 10 hours, one pump would take 20 hours to fill it on its own.
The next step is to calculate how many pumps would be needed to fill the reservoir in 4 hours. If one pump fills 1/20 of the reservoir per hour, then the number pumps needed to fill it in one hour would be 20. Therefore, to fill it in 4 hours, we would need 20/4 pumps, which is 5 pumps in total. Since we already have 2 pumps, we need an additional 3 pumps to fill the reservoir in 4 hours.