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Two ships start from points P and Q respectively towards each other and cross each other after 6 hours. The ship with greater speed (in still water) is running upstream and thus it covers 48 km less distance than the other ship when the two ships cross each other. Find the difference of speeds of two ships in still water. (The speed of the current is 6 km/hr.)

Two ships start from points P and Q respectively towards each other and cross each other after 6 hours. The ship with greater speed (in still water) is running upstream and thus it covers 48 km less distance than the other ship when the two ships cross each other. Find the difference of speeds of two ships in still water. (The speed of the current is 6 km/hr.) Correct Answer 4 km/hr

Suppose the speeds of ships are ‘x’ and ‘y’ km/hr (x > y);

Given speed of the current is 6 km/hr and the ship with greater speed (in still water) is running upstream;

∴ Speed of 1st ship = (x – 6) km/hr

Speed of 2nd ship = (y + 6) km/hr

Since two ships cross each other after 6 hours and 1st ship covers 48 km less than the 2nd;

∴ (x – 6) × 6 = (y + 6) × 6 – 48

⇒ 6x – 36 = 6y + 36 – 48

⇒ 6x – 6y = 24

⇒ (x – y) = 4 km/hr

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