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Difficulty: MediumCalculating Distance

A naval submarine travels completely submerged at a steady cruising speed of 40 knots40\text{ knots}. If it maintains this speed for 3 hours and 15 minutes3\text{ hours and } 15\text{ minutes} during a continuous sonar patrol, what is the total distance covered?

  1. A
    120 nautical miles120\text{ nautical miles}
  2. B
    126 nautical miles126\text{ nautical miles}
  3. 130 nautical miles130\text{ nautical miles}Answer
  4. D
    720 nautical miles720\text{ nautical miles}

Answer

130 nautical miles130\text{ nautical miles}
The correct answer is derived by converting the 15 minutes15\text{ minutes} into 0.25 hours0.25\text{ hours}, yielding a total continuous travel time of 3.25 hours3.25\text{ hours}. Multiplying the cruising speed of 40 knots40\text{ knots} by 3.25 hours3.25\text{ hours} results in exactly 130 nautical miles130\text{ nautical miles}.

Step-by-Step Solution

1
Identify the standard distance formula.
Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}
This formula connects speed, travel time, and distance covered.
2
Convert the mixed time measurement (3 hours and 15 minutes3\text{ hours and } 15\text{ minutes}) entirely into hours.
15 minutes÷60 minutes/hour=0.25 hours15\text{ minutes} \div 60\text{ minutes/hour} = 0.25\text{ hours}. Total time is 3+0.25=3.25 hours3 + 0.25 = 3.25\text{ hours}.
The rate is given in knots (nautical miles per hour), so the time must be strictly in hours before multiplication.
3
Multiply the rate by the total time in hours.
40×3.25=130 nautical miles40 \times 3.25 = 130\text{ nautical miles}
Applying the values to the distance formula yields the total traveled distance.

Key Concept

Calculating distance by standardizing mixed time units (hours and minutes) into a single metric before multiplying by rate.
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Topics

Calculating Distance

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