1.

A motorboat coverse a distance between two points in `4h` along the flow and in `8h` opposite to the flow. In how much time, distance can be covered in still water?

Answer» Let `d`: distance between two points
`v`: velocity of motorboat in still water
`u`: velocity of river flow
Along the flow : `v_(b//g)=v+u`
`d/(v+u)=4.........(i)`
`implies v+u=d/4.......(ii)`
Opposite to the flow : `v_(b//g)=v-u`
`d/(v-u)=8.........(iii)`
`implies v-u=d/8.......(iv)`
Time taken by boat to cover distance `d` in still water `t_(0)=d/v`.
Adding (ii) and (iv), we get
`2v=d/4+d/8=(3d)/8`
`d/v=16/3 h`
The motorboat will cover the distance in `16/3 h`.


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