Question

A steamer goes down stream from one
point to another in 7 hours. It covers the
same distance upstream in 8 hours. If the speed of stream be 2 km/hr, find the
speed of the steamer in still water and
the distance between the ports.
​

Answer 1

Given:

The stream speed = 2 km/hr

X km/hr is the steamer speed in still water.

Distance covered by Downstream in 7 hour = Distance covered by upstream in 8 hour

Consider below,

Downstream steamer speed= Still water steamer speed + Stream speed= x + 2

Upstream steamer speed = Still water steamer speed - Stream speed= x – 2

Distance covered by Downstream in 7 hour = 7(x + 2)

Distance covered by upstream in 8 hour = 8(x -2)

Solution:

7 (x + 2) = 8 (x - 2)

7x + 14 = 8x - 16

8x - 7x = 16 + 14

x = 30

Speed of the still water = 30 km/hr

Distance between the ports = 7 (30 + 1 ) = 7( 32 ) = 224 km.

Answer 2

Let the speed of the steamer in still water is x km/h and distance is d.  

Then, 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)          ......(1)

Distance covered by steamer downstream (d)=9(x+1)      ......(2)

From equation (1) and (2),

10(x−1)=9(x+1)

10x−10=9x+9

10x−9x=9+10

x=19 km/h

Substituting this value in equation(1),

Distance(d)=10(19−1)=180km

Hence, the speed of the steamer in still water is 19km/h and the distance between the ports is 180km.