Question

Two boats met at a point and one of them moves towards West while one towards South. After 2 hours, distance between them is 60 km. Find the speed of the slower boat if the difference in two speeds is 6 kmph.

Answer 1

Let the speed of the boat moving towards the West as x km/h and the speed of the boat moving towards the South as (x+6) km/h (since the difference in their speeds is 6 km/h).
After 2 hours, the boat moving towards the West would have covered a distance of 2x km, and the boat moving towards the South would have covered a distance of 2(x+6) km.
The distance between them is the hypotenuse of the right-angled triangle formed by their paths.
According to the Pythagorean theorem:
So, we have:
$(2x)^2+[2(x+6)]^2=60^2$
$4x^2+4(x+6)^2=3600$
$4x^2+4(x^2+12x+36)=3600$
$x^2+4x^2+48x+144=3600$
$8x^2+48x+144=3600$
$8x^2+48x−3456=0$
$x^2+6x−432=0$
$(x+24)(x−18)=0$
This gives two possible solutions: $x=−24$ or $x=18$.
Since speed cannot be negative, we discard the negative solution.

Therefore, the speed of the boat moving towards the West (slower boat) is $x=18\ km/h$.