A ship leaves on a long voyage . When it is 18 miles from the shore , a sea…
2024
A ship leaves on a long voyage . When it is 18 miles from the shore , a sea plane, whose speed is 10 times that of the ship is sent to deliver mail . How far from the shore does the sea plane catch up with the ship?
Answer: B. 20 miles — Solution: Let the speed of the ship be v miles/hour. Then the seaplane's speed is 10v miles/hour. Initial distance between the shore (where the plane starts)…
- A.
99 miles
- B.
20 miles
- C.
45 miles
- D.
35 miles
Attempted by 7 students.
Show answer & explanation
Correct answer: B
Solution:
Let the speed of the ship be v miles/hour. Then the seaplane's speed is 10v miles/hour.
Initial distance between the shore (where the plane starts) and the ship is 18 miles.
The relative speed at which the plane closes the gap is 10v - v = 9v.
Time to catch = distance / relative speed = 18 / (9v) = 2/v hours.
In that time the ship travels v * (2/v) = 2 miles further, so the meeting point is 18 + 2 = 20 miles from the shore.
Therefore the seaplane catches up with the ship 20 miles from the shore.