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Question
A steamer goes downstream and covers the distance between two ports in 3 hours. It covers the same distance in 5 hours when it goes upstream. If the stream flows at 3 km/hr, then find what is the speed of the steamer upstream?
Solution
Let speed of the steamer in still water be x km/h.
Speed of the stream = 3 km/h ...[Given]
Now, speed of the steamer downstream = (x + 3) km/h
And speed of the steamer upstream = (x – 3) km/h
According to the question,
Distance covered in 3 h by steamer downstream
= Distance covered in 5 h by steamer upstream
∴ 3(x + 3) = 5(x – 3) ...[∵ Distance = Speed × Time]
⇒ 3x + 9 = 5x – 15
⇒ 3x – 5x = – 15 – 9
⇒ – 2x = – 24
⇒ x = `- 24 xx ((-1)/2)`
∴ x = 12 km/h
Hence, the speed of the steamer upstream is (12 – 3), i.e. 9 km/h.
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