Two ships, one 200 metres in length and the other 100 metres in length, travel at constant but different speeds. When travelling in opposite directions, it takes 10 seconds for them to completely pass each other. When travelling in the same direction, it takes 25 seconds for them to completely pass each other. The speed of the faster ship, in metres per second, is
(A) 12
(B) 14
(C) 18
(D) 21
(E) 30
Solution

Let the speed of the faster ship be $x$ metres per second and the speed of the slower ship be $y$ metres per second.

When the ships are travelling in opposite directions, their relative speed is $(x+y) \mathrm{m} / \mathrm{s}$ and the distance required to pass is $300 \mathrm{~m}$, giving $10(x+y)=300$.

When the ships are travelling in the same direction, their relative speed is $(x-y) \mathrm{m} / \mathrm{s}$ and the distance required to pass is still $300 \mathrm{~m}$, giving $25(x-y)=300$.

Solving for $x$ gives $x=21$.

Thus, the speed of the faster ship is 21 metres per second.

ANSWER: (D)

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