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
Answers
(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:
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: