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 \(x=18\ km/h\).

Answer 2

Given information: - Two ships meet mid-ocean and then one goes south and the other goes west. 
- They travel at constant speeds. 
-Two hours later, they are 60 km apart. 
- The speed of one ship is 6 km/hour more than the other ship. 
To find: - The speed of the slower ship. 
Solution: Let's assume the speed of the slower ship as \( x\) km/hour. Then, the speed of the faster ship will be \((x+6) \) km/hour.
We know that distance = speed × time. 
After two hours, the distance travelled by the ship going south will be 2x and the distance travelled by the ship going west will be \(2(x+6).\) 
Using Pythagoras theorem, we can find the distance between the two ships after two hours: 
\((2x)^2 + (2(x+6))^2 = 60^2 \)
\(4x^2 + 4x^2 + 96x + 144 = 3600 \)
\(8x^2 + 96x - 3456 = 0 \)
\(x^2 + 12x - 432 = 0 \)
Solving the quadratic equation, we get:
\( x = 18\) or \(x = -24 \)
Since the speed of a ship can't be negative, the speed of the slower ship is 18 km/hour. Therefore, the correct answer is 18