Question

A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the streamer in still water and the distance between the ports.

Answer 1

Time taken downstream = 9 hour

and time taken upstream = 10 hour

Speed of stream = 1 km/h

Let the speed of a steamer in still water

= x km/h.

Distance downstream = 9 (x + 1) km.

and upstream = 10 (x - 1) km.

According to the condition,

10 (x - 1) = 9 (x + 1)

10x - 10 = 9x + 9 $\Rightarrow$ 10x - 9x = 9 + 10

$\Rightarrow$ x = 19

Hence speed of steamer in still water = 19 km/h

and distance = 9 (x + 1)

= 9 (19 + 1) = 9 $\times$ 20 km = 180 km. Ans.