# 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

• 28

let the speed of steamer in still water be n km/h

then, the speed downstream= (n+1) km/h

and the speed upstream= (n-1) km/h

the distance covered in 4 hrs while going downstream=speed X time

= {9(n+1)} km

= (9n+9) km

the distance covered in 5 hrs while going upstream      ={10(n-1)} km

=(10n-10) km

but each of the distance are between the two ports which is same.

thus,

9n+9=10n-10

9n-10n=-10-9

-n=-19

n=19

therefore, speed of the steamer in still water=n km/h=19km/h

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hope it helps.....

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Distance between the 2 ports = (n+1)9 = (19+1) 9= 180km

• 4

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 = – 109

⇒ – 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!

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thanks

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