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Difficulty: MediumRelative Motion and Catch-Up Scenarios

During a naval training exercise, a submarine travels submerged in a straight line at a constant speed of 1515 knots. Exactly 22 hours later, a destroyer departs from the same location and pursues the submarine along the exact same path at a constant speed of 2525 knots. How many hours will it take for the destroyer to overtake the submarine from the time the destroyer begins moving?

Answer: 3 hours

Answer

It will take 3 hours for the destroyer to catch up to the submarine.
To solve a catch-up scenario, first determine the initial distance between the two objects. The submarine travels at 1515 knots for 22 hours, creating a 3030 nautical mile gap. Next, find the relative speed by subtracting the slower speed from the faster speed (25−15=1025 - 15 = 10 knots) because they are moving in the same direction. Finally, divide the initial gap by the relative speed (30÷10=330 \div 10 = 3) to find the time it takes the destroyer to close the gap.

Step-by-Step Solution

1
Calculate the head-start distance of the submarine.
3030 nautical miles
The submarine travels at 1515 knots for 22 hours before the destroyer starts.
2
Calculate the relative catch-up speed.
1010 knots
The destroyer travels in the same direction, so the relative speed is the difference between their speeds (25−1525 - 15).
3
Calculate the time required to close the distance gap.
33 hours
Time equals distance divided by relative rate. Dividing the 3030 nautical mile gap by the relative speed of 1010 knots gives 33 hours.

Key Concept

Relative Motion and Catch-Up Scenarios
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Topics

Relative Motion and Catch-Up Scenarios

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