A large fish tank at an aquarium needs to be emptied so that it can be cleaned. When its large and small drains are opened together, the tank can be emptied in 2 hours. By
itself, it takes the small drain 3 hours longer to empty the tank than it takes the large
drain to empty the tank on its own. How much time would it take for each drain to empty
the pool on its own?

The draining time when only the big drain is opened is 2.303 hours.

The draining time when only the small drain is opened is 5.303 hours.

Step-by-step explanation:

From Physics, we know that volume flow rate (), measured in liters per hour, is directly proportional to draining time (), measured in hours. That is:

(Eq. 1)

Where is the proportionality constant, measured in liters.

From statement, we have the following three expressions:

(i) Large and small drains are opened

(Eq. 2)

(ii) Only the small drain is opened

(Eq. 3)

(iii) Only the big drain is opened

(Eq. 4)

By applying (Eqs. 3, 4) in (Eq. 2) and making some algebraic handling, we find that:

(Eq. 5)

Whose roots are determined by the Quadratic Formula:

and

Only the first roots offers a solution that is physically reasonable. Hence, the draining time when only the big drain is opened is 2.303 hours. And the time needed for the small drain is calculated by the following formula:

The draining time when only the small drain is opened is 5.303 hours.

answer: a

step-by-step explanation:

10.2 units

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e