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 steamer in still water and distance between the ports.​

Answer 1

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.

Answer 2

Given -

• Time taken by steamer (downstream) = 9 hours

• Time taken by steamer (upstream) = 10 hours

• Speed of steamer (in still water) = 1 km/hr

To find -

• Speed of steamer in still water.

Solution -

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

• Speed of steamer (upstream) = (x - 1)

• Speed of streamer (downstream) = (x + 1)

• Distance (upstream) = 10(x - 1)

• Distance (downstream) = 9(x + 1)

Making a linear equation -

• Time taken in downstream = Time taken in upstream.

→ 10(x - 1) = 9(x + 1)

→ 10x - 10 = 9x + 9

→ 10x - 9x = 9 + 10

→ x = 19

$\therefore$ The speed of steamer in still water will be 19 km/hr.

For distance :-

Distance = Distance of downstream.

D = 9 (x + 1)

D = 9(19 + 1)

D = 9 × 20

D = 180 Km

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