a garden hose can fill a pool in 3 days and a longer one can bill the pool in 2 days. How long will it take to fill the pool if both hoses are used.
In six days, the garden hose can fill 2 pools, and the longer one can fill 3 pools.
So in six days, both can fill five pools, or each pool takes 6/5 day
day in a half
To find out how long it will take to fill the pool when both hoses are used, we can use the concept of work rates. Let's assume the pool's capacity is C (in pool units) and the work rate of the first hose is r1 (in pool units per day), and the work rate of the longer hose is r2 (in pool units per day).
From the problem, we know that the first hose can fill the pool in 3 days, which means its work rate is 1/3 pool units per day (r1 = 1/3). Similarly, the longer hose can fill the pool in 2 days, so its work rate is 1/2 pool units per day (r2 = 1/2).
When both hoses are used, their work rates are combined, so we can add them together to find the combined work rate:
r_combined = r1 + r2
Substituting the values, we get:
r_combined = 1/3 + 1/2 = 2/6 + 3/6 = 5/6 pool units per day
Now, to find the time it will take to fill the pool using the combined work rate, we can use the formula:
time = C / r_combined
Substituting the given values, we get:
time = C / (5/6) = (6/5)C
So, it will take (6/5)C days to fill the pool when both hoses are used, where C is the pool's capacity.