Question

The speed of a boat in still water is 15km/hr. it needs four more hours to travel 63 km against the current of river than it needs to travel down the river. determine the speed of the current of the river.

Answer 1

4 km / hour.

Step-by-step explanation:

Let us assume that the speed of the current of the river is x km/hr.

So, The speed of the boat in the direction of the current is (12 + x) km/hr.

And the speed of the boat in the opposite direction of current is (12 - x) km/hr.

From the given condition we can write

$\frac{63}{12 - x} - \frac{63}{12 + x} = 4$

⇒ 63(12 + x - 12 + x) = 4(12² - x²)

⇒ 126x = 576 - 4x²

⇒ 2x² + 63x - 288 = 0

Hence, $x = \frac{ - 63 \pm\sqrt{63^{2} - 4(2)(-288) } }{2(2)}$

⇒ $x = \frac{- 63 + 79.2}{4}$ {Neglecting the negative root}

⇒ x = 4 km/hr. (Answer)