A ship leaves on a long voyage. When it is 18 miles from shore, a sea plane, whose speed is ten times that of the ship, is sent to deliver mail. How far from the shore does the sea plane catch up with the ship?

Solution (By Examveda Team)

A _______18miles_____B ___x(let)___C
Let the speed of the ship be 1 mile/h and then speed of the plane becomes 10 miles/h.
Let time t is taken to cover the distance x from point B to point C by ship.
Hence, in time t plane will cover (18 + x) miles.

Now,
$$\frac{{\text{x}}}{1} = \frac{{18 + {\text{x}}}}{{10}}$$
Or, 10x = 18 + x
Or, x = 2 miles.
Hence, ship will cover 2 miles in 2 hours and plane will cover 20 miles in same time.

Short method:
Relative speed = (10 - 1) = 9 miles/h.
hence, time taken to catch up the ship is 2 hours so distance covered by the ship = 20 miles.