Question

A steamer goes downstream from one part 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 streamer in still water and the distance between ports.

Answer 1

Answer:

Given,

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 hours.

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

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

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

For verification you can also put the value of "x" in equation 1,

D = 9(19 + 1)     [Substituting the value of x in Equation 1]

D = 171 + 9  = 180

Thus the distance between two ports is 180 cm

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