The Timuga swimming pool, of Manila City has two pumps it uses to fill the pool. If one pump takes 12 hours to fill the pool and the other pump alone takes 16 hours to fill the pool, how long will it take both pumps working together to fill the pool?
how much of the job does each pump do in an hour?
1/12 + 1/16 = 1/x
together they take x hours.
48
Here's what I got.
Amount of pool filled by both the pumps is
1/12 + 1/16 = 7/48
Use common ratios of (amount of pool)/(time):
(7/48)/1 = 1/x
Cross multiply:
x = 48/7 = 6.9 hours, or more precisely
6 hours, 51 minutes, and 26 seconds
To find how long it will take both pumps working together to fill the pool, we can use the concept of rates.
Let's first determine the rates at which each pump can fill the pool. If one pump takes 12 hours to fill the pool, its rate of filling would be 1 pool / 12 hours. Similarly, the second pump alone takes 16 hours to fill the pool, so its rate of filling would be 1 pool / 16 hours.
Now, to find the total rate at which both pumps can fill the pool when working together, we need to add up their individual rates. Therefore,
Total rate = Rate of first pump + Rate of second pump
Total rate = 1/12 + 1/16
To add these fractions, we need to find a common denominator:
Total rate = (4/48) + (3/48)
Total rate = 7/48
This means that when both pumps work together, they can fill 7/48 of the pool in one hour.
To find how long it will take to fill the entire pool, we can set up the equation:
(7/48) pool/hour * x hours = 1 pool
Solving for x, we get:
x = (1 pool) / (7/48 pool/hour)
x = 48/7 hours
Therefore, it would take approximately 6.857 hours (or approximately 6 hours and 52 minutes) for both pumps working together to fill the pool.