Question

17. A motor boat going downstream overcomes a float
at a point A. 60 minutes later it turns and after
some time passes the float at a distance of 12 km
from the point A. The velocity of the stream is
(assuming constant velocity for the boat in still
water)
(1) 6 km/h
(2) 3 km/h
(3) 4 km/h
(4) 2 km/h ​

Answer 1

(1)6 km/hr

Explanation:

Let the velocity of boat be x km/hr and the velocity of stream be y km/hr

Speed of the boat downstream = x+y

Distance covered by the boat after it passes the float(within 60 min or 1 hr)= (x+y) km

Distance covered by the float before the boat observes it the second time=12 km

Speed of float=y km/hr

Total time taken by the float=(12/y)hr

Time taken by the boat to reach the float after it turns back={(12/y)-1}hr

Speed of the boat upstream(after it turns back)=(x-y)km/hr

Distance covered by the boat after turning back= {(12/y)-1}(x-y)

ATQ,

x+y=12+{(12/y)-1}(x-y)

=>xy+y2=12y+12x-yx-12y+y2

=>2xy=12x

=>y=6 km/hr

Answer 2

Answer:

Dear student,

Let speed of stream be v and speed of motorboat be u.

Now distance moved by boat in 1 hour=(u+v)*1=u+v

total time is=6/v

speed of boat when it turns back=u-v

=>u+v-6=(u-v)(6/v -1)

solving for v we get, v=3 km/hr [Ans]

Regards,

Thank You,

Sneha Singh.

Explanation: