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Posted by: Surajit P. on 24.05.2022
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Answer:
Let the speed of the boat in still water = x km/hr
Let the speed of the current = y km/hr
Then the speed of the boat down stream (in favour of current) = x+y = u (say)
Speed of the boat in upstream(against the current) = x-y = v(say)
The distance traveled by the boat in downstream = 15 km
Time taken in downstream travel = 15/u
The distance traveled in upstream = 3km
Time taken in upstream travel = 3/v
Total time of travel in the boat = (15/u) +(3/v) = 4 hrs(given) ………. A
In the second instance distance traveled in downstream = 20kms
Time taken in downstream travel = 20/u
Distance traveled in upstream = 15 kms
Time taken in upstream travel = 15/v
Total time of travel in boat = (20/u)+(15/v) = 9 hrs (given) ………… B
We have (15/u) + (3/v) = 4
(20/u)+ (15/v) = 9 or (4/u) +(3/v) = 9/5
Eliminating v ,we get 11/u = 11/5 .Therefore u =5
Now putting this value in “A”, we get (15/5) + (3/v ) = 4 or
3/v = 4-3 = 1 .Therefore v = 3
Thus we have two new equations as below:
u= x+y = 5
v= x-y = 3
Eliminating y ,we get 2x = 8 or x =4
Hence the speed of the boat in still waters =x = 4 km/nr.
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