Determine whether quantities vary directly or inversely and find the constant of variation. It takes four identical water pumps 6 hours to fill a pool. How long would it take th…

Question

asked Aug 18, 2019 225k views

1 Answer

Joseph Ishak · Answer 1 · 2019-08-23T12:23:30+0000

Let the number of water pumps be n and the time taken to fill the pool is t.

Now, we can see that higher the number of water pumps, lesser the time to fill the pool.

It means quantities vary indirectly.

Thus,
$n=(k)/(t) , \text{ where k is the constant of variation}$

Now, we have been given that It takes four identical water pumps 6 hours to fill a pool.

Thus, we have

$4=(k)/(6) \\ \\ k=24$

Hence, constant of variation is 24.

Now, we have to find the time that three pumps will take to fill the same pool.

$3=(24)/(t) \\ \\ 3y=24\\ \\ y=(24)/(3) \\ \\ y=8$

Hence, it will take 8 hours to fill the pool by three identical pumps.