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A boat has speed of 15 m/s in still water, but going upstream its speed is half the speed going downstream. The boat is going downstream and a ship (also going downstream) crosses the boat in 15 seconds. The ship is double the length of the boat and is 100 meters long. Find the time the ship will take to cover 144 km while going upstream.

1. 1 hour
2. 2 hours
3. 1.33 hours
4. 1.6 hours

Correct answer: 2 hours

Solution

Stream speed c: 15-c=(15+c)/2 → 30-2c=15+c → c=5 m/s. Boat downstream=20 m/s, upstream=10 m/s. Ship length=100m (boat=50m, half of ship). Ship crosses boat from behind (both downstream): relative speed=(100+50)/15=10 m/s. Ship downstream=boat downstream+relative=20+10=30 m/s. Ship still water=30-5=25 m/s. Ship upstream=25-5=20 m/s. Time=144×1000/20=7200 s=2 hours.

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