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 three of these same pumps to fill the pool, assuming they all pump at the same rate?

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, [tex]n=\frac{k}{t} , \text{ where k is the constant of variation}[/tex]Now, we have been given that It takes four identical water pumps 6 hours to fill a pool. Thus, we have[tex]4=\frac{k}{6} \\ \\ k=24[/tex]Hence, constant of variation is 24.Now, we have to find the time that  three pumps will take to fill the same pool.[tex]3=\frac{24}{t} \\ \\ 3y=24\\ \\ y=\frac{24}{3} \\ \\ y=8[/tex]Hence, it will take 8 hours to fill the pool by three identical pumps.