A coastal patrol boat is conducting a surveillance mission. It travels at a steady speed o… — Armed Services Vocational Aptitude Battery (ASVAB)

A coastal patrol boat is conducting a surveillance mission. It travels at a steady speed of $12\text{ knots}$ (nautical miles per hour) for $2\text{ hours}$ and $15\text{ minutes}$ . It then increases its speed to $20\text{ knots}$ for $12\text{ minutes}$ to intercept a vessel. What is the total distance traveled by the patrol boat, in nautical miles?

A
$28.2$
$31$ Answer
C
$39.2$
D
$67$

Answer

The correct answer is

31

nautical miles.

The total distance is found by calculating the distance for each leg separately. First, convert the times into hours:

15\text{ minutes}

0.25\text{ hours}

(making the first leg

2.25\text{ hours}

), and

12\text{ minutes}

0.2\text{ hours}

. Multiplying these times by their respective speeds (

12 \times 2.25

and

20 \times 0.2

) gives distances of

27

and

4

nautical miles. Adding these together yields a total of

31

nautical miles.

Step-by-Step Solution

Convert the time of the first leg into hours.

2\text{ hours and } 15\text{ minutes} = 2 + \frac{15}{60} = 2.25\text{ hours}

Speed is given in knots (nautical miles per hour), so the time must be in hours to cancel the units properly.

Calculate the distance traveled during the first leg.

12\text{ knots} \times 2.25\text{ hours} = 27\text{ nautical miles}

Using the formula Distance = Rate x Time.

Convert the time of the second leg into hours.

12\text{ minutes} = \frac{12}{60} = 0.2\text{ hours}

Maintaining consistent units across all calculations.

Calculate the distance traveled during the second leg.

20\text{ knots} \times 0.2\text{ hours} = 4\text{ nautical miles}

Using the formula Distance = Rate x Time for the second segment.

Add the distances of both legs to find the total distance.

27 + 4 = 31\text{ nautical miles}

The total distance is the sum of the individual segments of the journey.

Key Concept

Calculating total distance for multi-leg journeys requires converting mixed time units into hours and applying the Distance = Rate x Time formula to each leg separately.

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