a steamer goes downstream from one point to another in 9 hours.it covers the same distance upstream in 10 hours.if the speed of the stream be 1km/hr,find the speed of the steamer in still water and the distance between the two ports?
Let the speed of steamer in still water be x km/h.
In the speed downstream he has advantage of 1km/h = (x+1) km/h
The speed in upstream where he has disadvantage of 1km/h = (x-1) km/h
The distance covered in downstream is 9 hrs = speed * time = {9(x+1)} km
= (9x+9) km
The distance covered in 10 hrs while going upstream ={10(x-1)} km
=(10x-10) km
Since the distance is same in both the cases
thus,
9x+9=10x-10
9x-10x=-10-9
-x=-19
x=19
therefore, speed of the steamer in still water= x km/h= 19km/h
Distance between the 2 ports = (x+1)9 = (19+1) 9= 180km
Distance = Speed × Time)