Question

A steamer goes down stream from one part to another in 9 hrs. It covers the same distance up steam in 10 hrs. If the speed of the stream is 1 km/hr. Find the speed of the steamer in still water.

Answer 1

Answer:

Step-by-step explanation:

Answer:

A steamer goes downstream. The distance between the two ports is 180 km.

Solution:

Let the speed of the streamer be ‘x’ and Distance be ‘D’

Given the speed of the stream is 1 km/hr.

Thus the downstream speed is given by ‘(x+1)’km/hr and the upstream speed is given by (x-1) km/hr.

Given that time taken to travel downstream is 9 hr

Therefore downstream distance = 9(x+1) …………..(Equation 1)

Again it is given that time taken to travel upstream is 10 hour.

Therefore upstream distance = 10(x-1)  ……………(Equation 2)

Since distance is same in both cases, we equate the upstream distance and downstream distance.

9(x+1) = 10(x-1)

9x + 9 = 10x - 10

9 + 10=10x - 9x

x = 19

Now substituting the value of "x" in any of the equation 1 or 2, we get

D = 10(19-1)     [Substituting the value of x in Equation 2]

D = 190-10  = 180

Thus the distance between two ports is 180 cm

Answer 2

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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)

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

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.