Water flows into a rectangular tank of plan dimensions 200 m by 160 m through a rectangular pipe of cross section 1.5 m by 1.25 m at a speed of 20 km per hour. In how many minutes will the water level in the tank rise by 2 m?

Introduction / Context:
This problem applies volume flow rate concepts to a practical situation of filling a large rectangular tank through a pipe. The idea is that the volume of water entering per unit time must equal the increase in volume of water in the tank per unit time. Once the required volume corresponding to a 2 m rise is known, we can divide that by the flow rate to find the required time.

Given Data / Assumptions:

• Tank length = 200 m.
• Tank breadth = 160 m.
• Required rise in water level = 2 m.
• Pipe cross section: 1.5 m by 1.25 m.
• Flow speed through pipe = 20 km per hour.
• No leakage or overflow is assumed.

Concept / Approach:
The key steps are:
1) Compute the volume of water needed to raise the tank level by 2 m: base area of tank * rise in height. 2) Compute the volumetric flow rate through the pipe: cross sectional area of pipe * flow speed. 3) Time required = required volume / flow rate. We must also convert the flow speed from km per hour to metres per minute so that the final time is in minutes.

Step-by-Step Solution:
Step 1: Compute the volume needed in the tank. Base area of tank = 200 * 160 = 32000 m^2. Required rise = 2 m. Required volume = 32000 * 2 = 64000 m^3. Step 2: Compute the pipe cross sectional area. Area of pipe = 1.5 * 1.25 = 1.875 m^2. Step 3: Convert flow speed to metres per minute. 20 km per hour = 20000 m per hour. Per minute = 20000 / 60 ≈ 333.33 m per minute. Step 4: Compute flow rate. Flow rate = 1.875 * 333.33 ≈ 625 m^3 per minute. Step 5: Compute time. Time = required volume / flow rate = 64000 / 625 = 102.4 minutes.

Verification / Alternative check:
We can check the magnitude: in about 100 minutes the water must fill 64000 m^3. A flow rate of 625 m^3 per minute for 100 minutes gives 62500 m^3, which is slightly less than 64000 m^3, so slightly more than 100 minutes is needed. The exact value 102.4 minutes is therefore reasonable and consistent with this quick mental estimate.

Why Other Options Are Wrong:
80 minutes and 96 minutes are too small, since they would not supply enough volume at 625 m^3 per minute to reach 64000 m^3.
120 minutes and 140 minutes are larger than necessary and would fill the tank beyond the 2 m mark if the flow continued for that long.

Common Pitfalls:
A frequent error is incorrect unit conversion for speed, such as using 20 m per minute instead of converting 20 km per hour correctly. Another mistake is forgetting that the tank is very large, which leads some learners to underestimate the time. Some students also miscalculate the area of the pipe or the tank base. Carefully tracking units and performing each multiplication step separately reduces these errors.

Final Answer:
The water level in the tank will rise by 2 m in approximately 102.4 minutes.