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?

Answer 1

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.