SOLUTION: A tank is filled with 360 liters of water. A hole at the bottom of the tank allows the water to drain at a constant rate of 0.2 liters per second. How many minutes will it take to

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Question 1207797: A tank is filled with 360 liters of water. A hole at the bottom of the tank allows the water to drain at a constant rate of 0.2 liters per second. How many minutes will it take to completely empty the tank?
Found 4 solutions by MathLover1, josgarithmetic, math_tutor2020, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Draining rate is .

For the given volume:


Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer: 30 minutes

Explanation

x = number of seconds that elapse

The tank starts off completely full at 360 liters.
The drain rate is a constant 0.2 liters per second.
After x seconds elapse, the tank loses 0.2x liters of water.
There are 360-0.2x liters remaining.

The tank is empty when 0 liters remain.
We'll set the previous expression equal to 0 to solve for x.

360-0.2x = 0
360 = 0.2x
x = 360/0.2
x = 1800
It takes 1800 seconds for the tank to completely empty.

Divide by 60 to convert from seconds to minutes.
1800 seconds = 1800/60 = 30 minutes is the final answer.


Side note:
I'm not too familiar with physics so I could be wrong, but I have a feeling that the water won't drain at a constant rate in reality.
I have a feeling it's more of a case of "more water --> faster drain rate" since gravity is pulling on more mass and hence more of a downward force is applied.
Regardless of this, it's probably best to stick to the assumption of a constant rate since the textbook stated as such. We're in a theoretical framework anyway.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

        My approach to such problems is  " solve as simple as it is possible ".
        If there is a simplest way,  it is preferable.

        This problem can be solved arithmetically,  without using fractions and without using equations.
        It is a good exercise to develop skills on counting and to develop common sense. 


A constant rate 0.2 liter per second means 1 (one) liter in 5 seconds.


So, the time to empty this tank is 360*5 = 1800 seconds.


To get minutes, divide 1800 seconds by 60 seconds, because 1 minute is 60 seconds.


ANSWER.  1800/60 = 180/6 = 30 minutes.

Solved.



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