It takes 2 minutes to get water from a well by a bucket which has a hole. Through the hole, 500 ml is wasted while water is being taken from the well ( capacity of the bucket is 3 liters). A tank is going to be filled by that bucket. The tank also has a hole and 500 ml of water leaks through it for each minute. ( Capacity of the tank is 50 liters ) How long it will take to fill the whole tank by the bucket

 In about 51 minutes, the tank may be momentarily filled, but until the leak is stopped, the whole tank will never remain filled.

Step-by-step explanation: There may be a way to calculate this using calculus, but I don't know that yet.

Here is my reasoning:

The 3L bucket will never be full, but every 2 minutes there will be 2.5 L that can be dumped into the tank.

The 50L tank would be full after 20 dumps. That's 50/2.5 = 20

20 dumps every 2 minutes will take 40 minutes.

During that 40 minutes, the tank leaks 8L.

8L takes another 3.2 buckets  to replace, taking 6.4 minutes.

In 6.4 minutes, the tank leaks .5 × 6.4 L, or 3.2 L

3.2L takes another 1.3 dumps in about 2.6 minutes.

At this point, the last bucket could be filled for the entire 2 minutes, and the additional .7L will be enough to momentarily fill the entire tank.

Adding all the times: 40 + 6.4 + 4 = 50.4

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

the radius is 2 times the diameter.

step-by-step explanation: