Question

A steamer goes downstream from one point to another in 9 hours. It cover the same distance upstream in 10 hours at the speed of the stream be 1 km per hour find the speed of the stream in still water and the distance between the ports

Answer 1

Dear Student!

Given, speed of the stream = 1 km/hr

Let the speed of steamer in still water be x km/hr.

Speed of the steamer downstream = Speed of steamer in still water + Speed of the stream = (x + 1) km/hr

Speed of the steamer upstream = Speed of steamer in still water – Speed of the stream = (x – 1) km/hr

Distance covered by the steamer downstream in 9 hours = 9 (x + 1) km
 (Distance = Speed × Time)

Distance covered by the steamer upstream in 10 hours = 10 (x – 1) km.

Distance covered by steamer downstream in 9 hours = Distance covered by steamer upstream in 10 hours

∴ 9 (x + 1) = 10 (x – 1)

⇒ 9x + 9 = 10x – 10

⇒ 9x – 10 = – 10 – 9

⇒ – x = – 19

⇒ x = 19

∴ Speed of steamer in still water is 19 km/hr.

Distance between the two ports = 9 (x + 1) km = 9 (19 +1) km = 9 × 20 km = 180 km

Cheers!

Answer 2

it's easy to solve...

here s be speed
so
Let the speed of steamer = s km/hr 
speed of stream = 1 km/hr 
so down stream resultant speed = (s + 1) km/hr 
& up stream resultant speed = (s – 1) km/hr 
Distance = speed × time 

Distance = speed × time 
= 9 (s + 1) = 10 (s – 1) 
9 s + 9 = 10 s – 10 
s = 10 + 9 = 19 km.hr speed of steamer. 
Distance travelled = 9(s + 1) =
9 × 20 = 180 km

hope it's helpful for you!