Question

A boatman can cover a river of 60 km length and came back at its initial point in 4.5 hrs.if speed of boat is thrice than that of the speed of stream then find the speed of boat

Answer 1

final velocity of boat=120/4.5km/h
.. =200/3km/h
velocity of boat=3speed of stream
speed of boat- speed of stream=200/3km/h
speed of boat-1/3 speed of boat=200/3
2/3 speed of boat=200/3
speed of boat=100km/h

Answer 2

Given data is the distance covered by the boat in one direction is 60km therefore the total distance covered is $2\times 60=120km,$ for which the total time spent is given as 4.5 hours.

Therefore the speed of boat assuming the speed of stream to be normal, is calculated by $speed=\frac { distance }{ time } \Rightarrow speed=\frac { 120 }{ 4.5 } =\frac { 80 }{ 3 } km/hr.$

Given situation states that the speed of boat be raised to thrice of speed of stream then, speed of boat with respect to speed of stream is to be calculated. Therefore,

Speed of boat - Speed of stream = Speed of boat relative to speed of stream $( S_bs ),$ i.e. new speed of boat = 3 speed of stream. Putting the values, we get –  $speed\quad of\quad boat - \frac { 1 }{ 3 } speed\quad of\quad boat = S_bs \Rightarrow S_bs =\frac { 2 }{ 3 } speed\quad of\quad boat \Rightarrow S_bs =\frac { 2 }{ 3 } (\frac { 80 }{ 3 }) = 53.3 km/h.$