Question

A boatman takes $5$ hours to go downstream and $10$ hours to come back to the same place. If the speed of the stream is $40$ km per hour, calculate the boating speed in still water.

Answer 1

Let, the boating speed in still water be x km / hr

We know for upstream the resultant speed is given by ( boat speed - speed of the stream )

Similarly for downstream we have ( boat speed + speed of the stream )

Moreover we know , Distance = speed X time

Now, he takes 5 hours in downstream

$\therefore D=5\times (x+40)$ [ speed of the stream is 40 km/hr (given) ]

$\therefore D=5x+200$

And for upstream he takes 10 hours.

$\therefore D=10\times (x-40)\therefore D=10x-400$

Since the distance is the same, we have,

5 x + 200 = 10 x - 400

or, 5 x = 600

$\Rightarrow$ x = 120

$\therefore$ The boating speed is 120 km / hr .