Question

A boat whose speed in the still water is 16 km/h covers a distance of 30km upstream and returns taking 4 hrs in total then what is the speed of the current

Answer 1

Answer:

4 km / hr

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Explanation:

Let v be the speed of the current in km/h ( v > 0 ).

The speed of the boat upstream is then 16 - v (16 relative to the water, but then losing v because the water is moving).

The time taken to travel upstream is then

time upstream = distance / speed = 30 / ( 16 - v )

The speed of the boat downstream is 16 + v.

The taken to travel back downstream is

time downstream = distance / speed = 30 / ( 16 + v )

Together, the total time is 4 hours so:

30 / ( 16 - v )  +  30 / ( 16 + v ) = 4

=> 30 ( 16 + v ) + 30 ( 16 - v ) = 4 ( 16 - v ) ( 16 + v )

=> 30 × 16 × 2 = 4 ( 16² - v² )

=> 240 = 16² - v²

=> v² = 256 - 240 = 16

=> v = 4  ( since v > 0 ).