If it takes a tub 20 minutes to fill up when the water is on all the way and 15 minutes to drain, how long will it take for the tub to be completely drained when the water is left all the way on?
In 1 hour the tub can fill up 3 times and the tub can drain 4 times. So will it take 45 minutes to be completely drained?
No. In 1 minute, 1/20 of the tub fills, while 1/15 drains. So, the net rate of filling is
1/20 - 1/15 = -1/60
So, in 60 minutes the full tub drains.
This assumes, of course, that the drain is opened when the tub is completely full.
You are right it takes 45 minutes
Anonymous you're wrong.
To determine how long it will take for the tub to be completely drained when the water is left on, we need to find the time it takes for one complete cycle of filling and draining.
Given that it takes 20 minutes to fill the tub and 15 minutes to drain, we can find the total time for one cycle by adding the time to fill and the time to drain: 20 minutes + 15 minutes = 35 minutes.
Now, let's consider how many cycles will occur in 1 hour. We know that in 1 hour, the tub can fill up 3 times and drain 4 times, resulting in a net drain of 1 tub. So, in 1 hour, it takes 4 cycles to drain the tub completely: 4 cycles x 35 minutes per cycle = 140 minutes.
Therefore, it will take 140 minutes, or 2 hours and 20 minutes, for the tub to be completely drained when the water is left on all the way.