if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long wil

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long will it take to fill up the pool using all 3 hoses?

Let V be the pool's Volume. Each hour, the hoses fill up this much of the pool:

• Hose A, V/6 of the pool
• Hose B, V/3 of the pool
• Hose C, V/2 of the pool

Effective fill rate is:
V/6 + V/3 + V/2
6V/36 + 12V/36 + 18V/36
36V/36 which is volume units per hour

Let t = units / rate
t = 1 hour, so we have:
t = units / rate
t = V (volume units) / V (volume units / hour)
t = 1 hour