No using algebra

You're right, Gareth! Let's solve this without using algebra.

a) How long will it take for the water levels in both tanks to become equal?

Step 1: Calculate the base area of each tank and convert flow rates to cubic centimetres per minute. $Base area of Tank C = 50 cm \times 30 cm = 1500 cm^2$ $Base area of Tank D = 40 cm \times 25 cm = 1000 cm^2$ $Flow into Tank C = 3 L/min \times 1000 cm^3/L = 3000 cm^3/min$ $Flow out of Tank D = 1 L/min \times 1000 cm^3/L = 1000 cm^3/min$

Step 2: Calculate the rate of change of water level for each tank. $Rate of level increase for Tank C = \frac{3000 cm^3/min}{1500 cm^2} = 2 cm/min$ $Rate of level decrease for Tank D = \frac{1000 cm^3/min}{1000 cm^2} = 1 cm/min$

Step 3: Determine the initial difference in water levels. Tank C starts at $12 \text{ cm}$. Tank D starts at $30 \text{ cm}$. $Initial difference in levels = 30 cm - 12 cm = 18 cm$

Step 4: Calculate the rate at which the difference between the water levels changes. Since Tank C's level is increasing and Tank D's level is decreasing, their levels are moving towards each other. The difference between them is closing at a combined rate. $Rate at which difference closes = 2 cm/min (Tank C) + 1 cm/min (Tank D) = 3 cm/min$

Step 5: Calculate the time it takes for the water levels to become equal. Divide the initial difference by the rate at which the difference closes. $Time = \frac{Initial difference}{Rate at which difference closes} = \frac{18 cm}{3 cm/min} = 6 minutes$ The water levels will become equal after 6 minutes. $Answer (a): \text{6 minutes}$

b) What will the common water level be then?

Step 6: Calculate the water level in either tank after 6 minutes. Using Tank C: $Final level in Tank C = Initial level + (Rate of increase \times Time)$ $Final level in Tank C = 12 cm + (2 cm/min \times 6 min) = 12 cm + 12 cm = 24 cm$ (Alternatively, using Tank D: $30 cm - (1 cm/min \times 6 min) = 30 cm - 6 cm = 24 \text{ cm}$) The common water level will be 24 cm. $Answer (b): \text{24 cm}$