it takes 18 hours to fill a pool using 8 garden hoses. How long would it take to fill the same pool using 9 garden hoses?
9/8 the hoses, so 8/9 the time: 16 hrs
or, since the same amount of work, measured in hose-hours, is done,
9x = 8*18
Well, if it takes 18 hours to fill the pool using 8 garden hoses, then I suppose you could find 9 people who are willing to stand around doing nothing for an hour while one lucky person gets to hold the extra hose. So, technically speaking, it would take 18 hours. But hey, think of all the great conversations they would have about water pressure and hose placement!
To find the time it would take to fill the pool using 9 garden hoses, we can set up a ratio using the number of hoses and the time it takes to fill the pool.
Let x represent the time it takes to fill the pool using 9 garden hoses.
The ratio between the number of hoses and the time it takes to fill the pool will remain constant.
So we can set up the following proportion:
8 hoses / 18 hours = 9 hoses / x
Using cross-multiplication, we can solve for x:
8x = 9 * 18
8x = 162
x = 162 / 8
x ≈ 20.25
Therefore, it would take approximately 20.25 hours to fill the same pool using 9 garden hoses.
To find out how long it would take to fill the pool using 9 garden hoses, we need to understand the relationship between the number of hoses and the time it takes to fill the pool.
Let's consider that using 8 hoses takes 18 hours to fill the pool. We can conclude that, on average, each hose contributes 1/8th of the total filling rate. Therefore, if we were to remove one hose, the filling rate would decrease by 1/8th.
Now, let's calculate how long it would take to fill the pool using only 1 hose. Since 8 hoses contribute to the entire filling rate, it would take 8 times longer to fill the pool with just one hose. Thus, it would take 18 x 8 = 144 hours to fill the pool with a single garden hose.
Finally, let's determine how long it would take to fill the pool using 9 hoses. Adding one more hose means increasing the filling rate by 1/8th. Therefore, the new filling rate would be 1/8th higher than the initial rate.
Using the initial filling rate, we found that it took 144 hours with 1 hose. To find the time it takes with 9 hoses, we need to reduce this time by 1/8th of the initial time:
144 hours - (1/8) x 144 hours = 144 hours - 18 hours = 126 hours.
So, using 9 garden hoses, it would take approximately 126 hours to fill the same pool.