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.
Answers
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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