[Guest]

Imagine a swimming pool 10 feet deep. Spout A can fill the tank in 1 hour and Spout B can fill the tank in 2 hours. There are 3 drain pipes, all near the bottom, and all connected to sensors. Drain C can drain the tank in 3 hours if it was continuous turned on, but only turns on at the 2 feet from the bottom mark. Drain D can drain the tank in 2 1/2 hours if it was continuous turned on, but only turns on at the 4 feet from the bottom mark. Drain E can drain the tank in 1 1/2 hours if it was continuous turned on, but only turns on at the 6 feet from the bottom mark.

All spouts and drains are turned on, with the spouts starting to fill the tank and no drains being activated until the water reaches the indicated heights.

How long until Drain C turns on?

How long until Drain D turns on?

How long until Drain E turns on?

How long until the water reaches the top?

When the water reaches the top, the spouts are turned off. How long until the pool is drained?

If you didn't want the water to reach the top, you could add a Drain F with a sensor that turns it on at the 9 foot mark. How fast would Drain F have to drain the pool if it was continuously turned on?

[Guest]

8min

Just over 18min

Almost 34min

Almost 233min

43.5min

8hrs 15min for the entire pool

[Guest]

Drain C turns on in 8 minutes

Drain D turns on in 18 min 17,1 sec

Drain E turns on in 33 min 35,4 sec

The water reaches the top in 4 hours 33 min 35,4sec

The pool is drained in 42 min 51,43 sec

Drain F would have to drain the tank in 10 hours.

[Guest]

Nobody has all answers correct yet. But, it's a very good start! Will post which ones are right/wrong and spoiler for correct answers later or tomorrow.

[bonanova]

In 90 hours,

A will fill 90 pools; B will fill 45 pools.

Combined fill rate is 135 pools/90 hours = 1.5 pools/hr

If the drains are on,

C drains 30 pools, D drains 36 pools, E drains 60 pools.

Combined drain rate is 126 pools/90 hours = 1.4 pools/hr

Combined, they drain a full pool in 1/1.4 = .714... hours.

Drain F would have to drain at a rate of at least .1 pool/hour.

Or take at most 10 hours to drain a full pool.

Let the pool fill.

Until C activates, net fill rate is 135/90 pools/hr. C activates in 90/135 x .2 = .133.. hours . Then,

until D activates, net fill rate is 105/90 pools/hr. D activates 90/105 x .2 = .1714.. hours later. Then,

until E activates, net fill rate is 69/90 pools/hr. E activates 90/69 x .2 = .2608.. hours later. Then,

after E activates, net fill rate is 9/90 = .1 pool/hour. Pool fills 90/9 x .4 = 4 hours later.

Total fill time is 4.56563147... hours. = 4 hours 33 minutes 56.273... seconds.

[Guest]

Fill Rate of A & B: .25ft per minute

To reach 2', 8 minutes.

Fill Rate reduced by: .0833ft/min

To reach 4' (2' at this new rate)

10 minutes 17 seconds,

Current Total Time: 18 minutes, 17 seconds.

To reach 6' (rate reduced by .0556)

15 minuets, 39 Seconds

Current Total Time: 33 minutes, 56 seconds

To reach 10' (rate reduced by .06667)

4 hours

Current Total Time: 4 hours, 33 minutes, 56 seconds.

To drain from 10' using C,D,E

Rate of 1/18 + 1/15 + 1/9 = .2333 ft / min

10 / .2333 = 42 minutes, 51 seconds

If you want the pool to stay at 9' A+B = C+D+E+F

A+B = .25

C+D+E = .2333

.25-.2333 = .01667 ft/min

Equivalent Drain Time: 10hrs.

[Guest]

Imagine a swimming pool 10 feet deep. Spout A can fill the tank in 1 hour and Spout B can fill the tank in 2 hours. There are 3 drain pipes, all near the bottom, and all connected to sensors. Drain C can drain the tank in 3 hours if it was continuous turned on, but only turns on at the 2 feet from the bottom mark. Drain D can drain the tank in 2 1/2 hours if it was continuous turned on, but only turns on at the 4 feet from the bottom mark. Drain E can drain the tank in 1 1/2 hours if it was continuous turned on, but only turns on at the 6 feet from the bottom mark.

C: 8 min

D: 18 min 18 sec

E: 33 min 57 sec

top: 4hrs 33 min 57 sec.