A fountain has two drainage valves. With only the first valve open, the fountain completely drains in 4 hours. With only the second valve open, the fountain completely drains in 5.25 hours. About how many hours will the fountain take to completely drain with both valves open?

Answer: it will take about 2.32 hours for the fountain to completely drain with both valves open

Step-by-step explanation:

The fountain has two drainage valves, First valve and second valve.

With only the first valve open, the fountain completely drains in 4 hours. This means that the rate at which the first valve drains is at a rate of 1/4 per hour

With only the second valve open, the fountain completely drains in 5.25 hours. This means that the rate at which the second valve drains is at a rate of 1/5.5 per hour

If both valves are opened, the fountain will drain faster but both valves will still be draining at their individual unit rates. They will be draining simultaneously. It means that their individual unit rates are additive ... Assuming it takes t hours to drain completely if both valves are open. Then their combined unit rate will be 1/t per hour. Therefore

1/4 + 1/5.5 = 1/t

9.5/22 = 1/t

t = 22/9.5 = 2.32 hours