A ship is approaching towards a shore, when it is 32 miles from the shore, a…
2024
A ship is approaching towards a shore, when it is 32 miles from the shore, a plane having speed 15 times that of the ship is sent to deliver supplies. How far from sea shore does the sea plane catches up with the ship?
- A.
30 miles
- B.
25 miles
- C.
15 miles
- D.
10 miles
Attempted by 4 students.
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Correct answer: A
Let x be the distance from the shore where the plane catches up with the ship. The ship starts 32 miles away and travels (32 - x) miles towards the shore. The plane starts from the shore and travels x miles to meet the ship. Since they travel for the same amount of time, the ratio of their distances equals the ratio of their speeds. Given the plane's speed is 15 times the ship's speed, we have x / (32 - x) = 15. Solving for x: x = 15(32 - x) => x = 480 - 15x => 16x = 480 => x = 30. Thus, the plane catches up with the ship 30 miles from the shore.