Final answer:
The capacity of the tank is found by establishing the rate at which the tank empties with the leak and the tap on. Solving the equation (L/28 - 2.5) * 42 = L leads to discovering the capacity of the tank is 210 liters.
Step-by-step explanation:
To find the capacity of the tank, we first need to understand that the leak by itself can empty the tank in 28 minutes, which means, if we let L be the capacity of the tank in liters, the rate of the leak would be L/28 liters per minute.
When the tap is also turned on, delivering 2.5 liters per minute, the tank becomes empty in 42 minutes. The combined rate of emptying the tank when the tap is on would be the leak rate minus the fill rate due to the tap, which is (L/28 - 2.5) liters per minute.
This rate times 42 minutes would equal the tank's capacity since the tank becomes empty in that time. Setting up the equation (L/28 - 2.5) * 42 = L and solving for L gives us:
L/28 * 42 = L + 2.5 * 42
L = L + 105
This is a contradiction, which hints at an error made during the process. Rethinking our steps, we should multiply the combined rate by the time the tank takes to empty when the tap is running to find the tank capacity. The correct equation is:
L = (L/28 - 2.5) * 42
Multiplying both sides by 28 to remove fractions, we get:
28L = L*42 - 105*28
By bringing all terms involving L to one side and constant terms to the other, we can solve for L:
28L - L*42 = -105*28
-14L = -105*28
L = (105*28)/14
L = 210 liters
Therefore, the capacity of the tank is 210 liters (Option B).