Question

a steamer goes downstream from one point to another in 9 hours. it covers the same distance up-stream in 10 hours. if the speed of the stream be 1 km / hour find the speed of the stream in still water and the distance between the ports.

Answer 1

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

given speed of steam =1 km/h

therefore, the speed of streamer downstream = (x +1) speed streamer upstream =(x-1)

distance covered by a steamer downstream = 9 (x+1)

distance covered by a streamer,upstream=10 (x-1)

according to given ,
9 (x+1)=10 (x-1)
9x+9=10x-10
9+10=10x-9x
19=x
x=19

distance between the ports = 9 (19+1)
=9 (20)
=180 km
hence, the speed of streamer in still water is 19 km/h and distance between the ports is 180 km.

Answer 2

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