Question

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?​

Answer 1

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 ! :)