Question

A man can row 4 kmph is still water. if the river is running at 2 kmph it takes 90 min to row to a place and back. how far is the place?

Answer 1

Let the distance between man and observation point is x km.
speed of man in still water = 4km/h
speed of river = 2km/h
so,speed of man in downstream =(4 + 2)= 6km/h
and speed of man in upstream = (4 - 2) = 2km/h

we know, time = distance/speed
now,time taken in downstream + time taken in upstream = 90 min = 3/2 hrs
=> x/6 + x/2 = 3/2
=> (x + 3x)/6 = 3/2
=> 4x/6 = 3/2
=> x = 3/2 × 6/4 = 18/8 = 9/4 = 2.25 km

hence, 2.25 know far from the place.

Answer 2

Let the distance between the two places be x

SO,

Relative speed of boat when it travels in direction of river = 4 + 2

= 6 km/hr

Relative speed of boat when it travels opposite to direction of river = 4 - 2

= 2 km/hr

Now,

Displacement = (Velocity )/ Time

Time = (Displacement )/ (Velocity)

Total time taken = 90 min

=90/60 = 3/2 hrs

By the relation,

x/6 + x/2 = 3/2

( 2x + 6x )/12 = 3/2

8x = 18

x= 9/4

x= 2.25

Hence the distance between the two place is 2.25 km