A soldier fires 7 shots from a gun in 14 minutes at a constant rate. If he continues firing at the same rate, how many shots will he fire in 3/2 hours (that is, in 1 hour 30 minutes)?

Introduction / Context:
This is a simple proportionality problem involving a constant rate of firing shots from a gun. The soldier fires at a steady rate and we scale that rate up to a longer time interval to determine how many shots he will fire in total.

Given Data / Assumptions:

• The soldier fires 7 shots in 14 minutes.
• His rate of firing is constant over time.
• We are asked to find how many shots he fires in 3/2 hours.
• 3/2 hours is equivalent to 1.5 hours or 90 minutes.

Concept / Approach:
When a rate is constant, the quantity produced is directly proportional to time. We first calculate the soldier's rate in shots per minute from the given 14 minute interval. Then we convert 3/2 hours into minutes and multiply the rate by this total time to get the total number of shots fired in that period.

Step-by-Step Solution:
The soldier fires 7 shots in 14 minutes. Rate of firing = 7 shots / 14 minutes = 0.5 shot per minute. Convert 3/2 hours to minutes: 3/2 hours = 1.5 hours. 1.5 hours = 1.5 * 60 = 90 minutes. Total shots in 90 minutes = rate * time = 0.5 shot per minute * 90 minutes. This equals 45 shots. Therefore, the soldier will fire 45 shots in 3/2 hours.

Verification / Alternative check:
Another way to see this is to note that 90 minutes contains 90 / 14 blocks of 14 minutes. In each 14 minute block, the soldier fires 7 shots. So total shots = 7 * (90 / 14) = (7 * 90) / 14 = 630 / 14 = 45 shots. This matches the earlier calculation and confirms the result.

Why Other Options Are Wrong:
44 shots would require a slightly smaller rate than 0.5 shot per minute, which contradicts the given data. 46 and 47 shots would require a slightly higher firing rate than stated. 42 shots is based on a rate of 0.4667 shots per minute, which does not match the basic proportion of 7 shots in 14 minutes.

Common Pitfalls:
A frequent error is misinterpreting 3/2 hours as 3 minutes or 2 hours instead of 1.5 hours. Another trap is in the unit conversion, where some learners use 3/2 * 14 directly without recognising that the reference interval is 14 minutes and the target interval is in hours. Always convert all times to the same unit, here minutes, before applying proportions.

Final Answer:
The soldier will fire 45 shots in 3/2 hours.