SOLUTION: A tank containing 50 litres of water develops a leak and loses water at a constant rate. After 20 minutes it contains 40 litres. After further 30 minutes the tank is 5% of its full

Question 1169754: A tank containing 50 litres of water develops a leak and loses water at a constant rate. After 20 minutes it contains 40 litres. After further 30 minutes the tank is 5% of its full capacity. Determine the tank's capacity.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Three points (x,y):
(0,50), (20,40), (30,0.05C) and C is for tank's capacity.

* MISTAKE FOUND: "After further 30 minutes,..."
That meant, 20+30=50 minutes.
The variable point should be (50,0.05C).

----------------NO, NOT THIS--------------------
slope, ;

To find C, use the unknown point.
------------solve this for C.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

From first two sentences, we have this equation V(t) = 50 - a*t. representing the current volume V(t) as a function of time, t, in minutes, and "a" is the constant leaking rate in liters per minute. At t= 20 minutes, V(20) = 40 = 50 - a*20, which gives a = = = 0.5 liters per minute. After further 30 minutes, the volume of the water in the tank is V(50) = 40 - 0.5*30 = 40 - 15 = 25 liters. So, 25 liters is 5% of the tank capacity. Hence, the total capacity of the tank is = 500 liters. ANSWER. The total capacity of the tank is = 500 liters.

Solved, answered, explained and completed.

/\/\/\/\/\/\/\/\

Do not accept nothing from the post by @josgarithmetic,

since he interprets the problem's description incorrectly.

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