Question

A steamer going downstream traveled the distance between two ports in 3 hours. The return trip took 3 hours 40 minutes. Find the speed of the water current if the speed of the steamer in still water is 18 mph.

Answer 1

let the speed of water current is x km/h and distance between two ports is y km

given, speed of the streamer in still water = 18 km/h

net speed in downstream = (x + 18)km/h

net speed in upstream = (18 - x) km/h

a/c to question,

time taken in downstream = 3 hours

or, y/(x + 18) = 3

or, y/3 = x + 18 ......(1)

time taken in upstream = 3 hours 40 minutes = 3 + 40/60 = 3 + 2/3 = 11/3 hrs

or, y/(18 - x) = 11/3

or, 3y/11 = 18 - x .......(2)

adding equations (1) and (2),

y/3 + 3y/11 = 36

or, (11y + 9y)/33 = 36

or, 20y/33 = 36

or, 5y/33 = 9

or, y = 33 × 9/5 = 297/5 = 59.4 km

from equation (1),

(59.4)/3 = x + 18

or, 19.8 - 18 = x

or, x = 1.8 km/h

Answer 2

Answer:

Let the distance between the two ports be x km.

Then, speed downstream = x/4

And speed upstream = x/5

Speed of the stream,

= [speed downstream - speed upstream] / 2

= (x/4 - x/5)/2

Or, (5x -4x)/40 = 2

Or, x/40 = 2

Thus, x = 80 km.

Distance between two ports = 80 km.