Question

A steamer Travels 90 km downstream in the same time as it takes to travel 60 km upstream in the speed of the stream is 5 km per hour find the speed of the steamer in still water

Answer 1

----------------------------------------

Here is the solution:

----------------------------------------

Let x be the speed of the steamer in still water

Speed of the stream = 5km/h (Given)

Downstream:

Speed = (x + 5)

Time = Distance ÷ speed

Time = 90 /( x + 5)

Upstream:

Speed = ( x - 5)

Time = Distance ÷ Speed

Time = 60/( x - 5)

Since the time taken for upstream and downstream is the same:

90 /( x + 5) = 60/( x - 5)

90 (x - 5) = 60 (x + 5)

90x - 450 = 60x + 300

30x = 750

x = 25 km/h

Answer: The speed of the steamer in still water is 25km/h

Answer 2

We will assume the speed of the boat as B and the Speed of current as C

speed of downstream = (B + C) Km/h

speed of upstream = (B - C) Km/h

We are given,

time = distance /speed

so, time taken in downstream + time taken in upstream = 12 h

90/(B + C) + 70/(B - C) = 12 ----(1)

Time taken in downstream = 9 h

72/(B + C) = 9

B + C = 8 km/h---------(2) , put it in equation (1)

90/8 + 70/(B -C) = 12

45/4 + 70/(B - C) = 12

70/(B - C) = 12 - 45/4 = 3/4

B - C = 280/3 km/h -------(3)

Now we will solve both equations (2) and (3),

2B = 280/3 + 8 => B = 140/3 + 4 = 152/3 km/h

now we will Put B in equation (2) ,

C = 8 - 152/3 = (24-152)/3 = -128/3 km/h

here , negative sign shows that Current is just opposite side of our assumption

So speed of current = -128/3 km/h