A naval supply ship leaves port heading due east at a constant speed of 24 knots. Exactly … — Armed Services Vocational Aptitude Battery (ASVAB)

A naval supply ship leaves port heading due east at a constant speed of $24$ knots. Exactly $1$ hour and $45$ minutes later, a destroyer leaves the same port to intercept the supply ship, traveling on the exact same course at a constant speed of $36$ knots. How many hours will it take for the destroyer to catch up with the supply ship, measured from the moment the destroyer leaves port?

Answer: 3.5 / 3.5 hours / 3 1/2 / 3 1/2 hours / 3.5 hrs / 7/2

Answer

3.5

The destroyer must close an initial gap of

42

nautical miles. Since it travels

12

knots faster than the supply ship, it closes the gap at a relative rate of

12

knots, which takes exactly

3.5

hours.

Step-by-Step Solution

Convert the head start time from hours and minutes into a decimal or fraction of hours.

1

hour and

45

minutes =

1.75

hours (or

\frac{7}{4}

hours).

Time units must properly match the speed units (knots, which are nautical miles per hour) before calculating distance.

Calculate the distance the supply ship traveled during its head start.

24 \text{ knots} \times 1.75 \text{ hours} = 42 \text{ nautical miles}

This establishes the initial gap distance the destroyer needs to close.

Determine the relative speed at which the destroyer is closing the gap.

36 \text{ knots} - 24 \text{ knots} = 12 \text{ knots}

Because both ships are traveling in the same direction, you subtract the slower speed from the faster speed to find the catch-up rate.

Calculate the time required to close the gap.

\frac{42 \text{ nautical miles}}{12 \text{ knots}} = 3.5 \text{ hours}

Time equals distance divided by rate. The gap distance divided by the relative speed gives the exact time to intercept.

Key Concept

Relative Motion and Catch-Up Scenarios

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