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

Explanation

The speed of the stream `=1`km/hr.
Let the speed of the steamer in still water be `x` km/h
Speed of steamer downstream `(u)=` speed of steamer in still water`+`speed of stream`=x+1`
Speed of steamer upstream `(v)=`speed of steamer in still water`-`speed of stream`=x−1`
Distance covered by steamer upstream `(d)=10(x−1)`
Distance covered by steamer downstream `(d)=9(x+1)`
According to the question:
`10(x−1)=9(x+1)`
`10x−10=9x+9`
`10x−9x=9+10`
`x=19` km/h
`therefore` The speed of the steamer in still water `=19`km/h
The distance between the ports `=10(x−1)=10(19-1)=18times10=180`km.