Answer to Question #177005 in Differential Equations for daniel wagaye

Question

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

Answer 1

Let $x$ is the speed of the current of the river.

Time against the current minus time down the river is 4.

Equation:

$\frac{63}{15-x}-\frac{63}{15+x}=4$

Then we multiply equation by $15^2-x^2=(15-x)(15+x)$ :

$63(15+x)-63(15-x)=4(15^2-x^2)$

$4x^2+126x-4*225=0$

$2x^2+63x-450=0$

$x=\frac{-63+\sqrt{63^2+4*2*450}}{2}=$

$=\frac{-63+\sqrt{3969+3600}}{4}=$

$=\frac{-63+87}{4}=6$

Answer: $x=6$