A house can fill the pool in 4 hours and another hose can fill the pool in 6 how long would it take to fill the pool with both hoses
(t / 4) + (t / 6) = 1
use 12 as common denominator ... (3 t / 12) + (2 t / 12) = 1
5 t / 12 = 1 ... 5 t = 12
Take the product of 2 numbers and divide by the sum of 2 number
(6×4)÷(6+4)
=2.4
To solve this problem, we need to calculate the combined rate at which both hoses fill the pool.
Let's say the rate at which one hose fills the pool is "x" pools per hour. Therefore, the rate at which the other hose fills the pool is "y" pools per hour.
We know that the first hose can fill the pool in 4 hours, so its rate is 1 pool / 4 hours, or 1/4 pools per hour. Similarly, the second hose can fill the pool in 6 hours, so its rate is 1 pool / 6 hours, or 1/6 pools per hour.
To find the combined rate, we add the rates of both hoses: x + y = 1/4 + 1/6
Now, we can find a common denominator for 4 and 6, which is 12. So, the combined rate is: x + y = 3/12 + 2/12
Simplifying the equation: x + y = 5/12
To find the time it takes to fill the pool with both hoses, we can assume that it takes "t" hours.
Using the combined rate formula, we have t * (x + y) = 1
Substituting the value of the combined rate, we get: t * (5/12) = 1
Now, we can solve for "t":
t = 12/5
Therefore, it would take approximately 2.4 hours (or 2 hours and 24 minutes) to fill the pool with both hoses.