One pump can fill a reservoir in 60 hours. another pump can fill the same reservoir in 80 hours. a third pump can empty the reservoir in 90 hours. if all three pumps are operating at the same time, how long will it take to fill the reservoir?
answer asap. you.

55.384 hours or 55 minutes and 23 seconds.

Step-by-step explanation:

You know that the filling rate of first pump is:

The filling rate of second pump is:

Since the third pump can empty the reservoir in 90 hours, the rate is:

Where "t" is the time in hours that will take fill the reservoir if all the three pumps are operating at the same time.

Knowing this, you can set up the following equation:

Finally, you must solve for "t". You get:

(55.384 hours or 55 minutes and 23 seconds)

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)