Solve the problem.
-A water tank can be filled in 5 minutes and emptied in 8 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?
A) $13 \frac { 1 } { 3 }$ minutes
B) $3 \frac { 1 } { 13 }$ minutes
C) $\frac { 1 } { 13 }$ minutes
D) $\frac { 1 } { 40 }$ minutes

Question

Quizplus · Accepted Answer

Let's assume that the tank has a capacity of 40 liters (just to make the calculation easier). When the tank is filled, it gains 8/5 liters per minute (that is, 1.6 liters per minute). When the tank is emptied, it loses 5/8 liters per minute (that is, 0.625 liters per minute).

Now, let's say the tank is being filled for x minutes (with the drain accidentally left open), so the amount of water in the tank after x minutes would be:

filled - emptied = 1.6x - 0.625x = 0.975x

Since the tank has a capacity of 40 liters, we can set up an equation:

0.975x = 40

Solving for x:

x = 40/0.975 = 41.03

Rounding to the nearest 1/3 minute (since that's the closest answer choice), we get:

x = $13 \frac { 1 } { 3 }$ minutes

Therefore, the answer is A) $13 \frac { 1 } { 3 }$ minutes.

Solve the Problem 131313 \frac { 1 } { 3 }1331​

Solve the Problem $13 \frac { 1 } { 3 }$