A boat sails down the river for 10 km and then up
the river for 6 km. The speed of the river flow is
1 km/h. What should be the minimum speed of the
boat for the trip to take a maximum of 4 hours?
Answers
Given:-
- A boat sails down the river for 10 km and then up the river for 6 km.
- The speed of the river flow is 1 km/h.
To find:-
- What should be the minimum speed of the boat for the trip to take a maximum of 4 hours?
Solution:-
Let speed of boat in still water is 'x' kmph.
Then,
Upstream speed = (x -1) kmph
Downstream speed = (x+1) kmph
We know :
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❥Time=distance/speed
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Acc to question :
Total time = 10 /(x+1) + 6/(x-1) = 4 (Given)
=> 10(x-1) + 6(x+1) / (x-1)(x+1) = 4
[(a+b)(a-b) = a²-b²]
=> 10(x-1)+6(x+1) / x²-1 = 4
=> 10(x-1)+6(x+1) = 4 (x²-1 )
=> 16x-4 = 4x² - 4
=> 16x = 4x²
=> x = 4 kmph .
Crosscheck:-
❥ Distance / speed = time
10 / ( x + 1 ) = 10/(4+1) = 2 hours...(1)
6/(x-1) = 6/(4-1) = 2 hours....(2)
Adding (1) & (2) ,
Total time = 2 + 2 = 4 hours .
Hence approved !
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AnswEr :- The minimum speed of the boat for the trip to take a maximum of 4 hours is 4 kmph .
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HOPE IT HELPS ! :)