How long will it take for the tub to completely empty with thte drain open and the water running at full speed?
Given: it takes 20 minutes to fill the tub and 15 minutes to drain the tub when the water is on all the way, full speed.
1/20 - 1/15 = -1/60
So, 1/60 of the tub drains every minute.
. . .
how'd you get 1/20-1/15?
To determine how long it will take for the tub to completely empty with the drain open and the water running at full speed, we need to compare the rates at which the tub fills and drains.
Given that the tub takes 20 minutes to fill and 15 minutes to drain, we can establish the rates as follows:
- Filling rate: 1 tub / 20 minutes
- Draining rate: 1 tub / 15 minutes
To find the time it takes for the tub to empty, we need to find the time at which the draining rate equals the filling rate.
Let's consider the rates at which the tub empties and fills in terms of tubs per minute:
- Emptying rate: 1 tub / 15 minutes = 1/15 tubs per minute
- Filling rate: 1 tub / 20 minutes = 1/20 tubs per minute
To determine when the tub will be completely empty, we need to find the time when the emptying rate equals the filling rate. This can be done by finding the reciprocal of the sum of the rates:
1 / (1/15 + 1/20)
To calculate this:
First, find the least common denominator (LCD) for 15 and 20, which is 60.
Then rewrite the rates in terms of the LCD:
1 / (4/60 + 3/60)
Combine the fractions:
1 / (7/60)
To divide by a fraction, invert and multiply:
1 * (60/7)
Which simplifies to:
60/7
So, it will take approximately 8.57 minutes (or approximately 8 minutes and 34 seconds) for the tub to completely empty with the drain open and the water running at full speed.