Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is

Question

Accepted Answer

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743537512/aptidude_questions/imjh7yr4vtnxrv56cwxo.png)

1. **Define Variables:**  
   Let the speed of the slower ship be $$x$$ km/hour. Then the speed of the faster ship is $$x + 6$$ km/hour.

2. **Distance Traveled in 2 Hours:**  
   - Distance traveled by the slower ship: $$2x$$ km.  
   - Distance traveled by the faster ship: $$2(x + 6) = 2x + 12$$ km.

3. **Use Pythagorean Theorem for Distance Between Ships:**  
   The ships form a right triangle with their paths as perpendicular sides and the distance between them as the hypotenuse. Using the Pythagorean theorem:  
   $$
   (2x)^2 + (2x + 12)^2 = 60^2
   $$

4. **Simplify Equation:**  
   Expand and simplify:  
   $$
   4x^2 + (4x^2 + 48x + 144) = 3600
   $$  
   Combine terms:  
   $$
   8x^2 + 48x + 144 = 3600
   $$  
   Simplify further:  
   $$
   8x^2 + 48x - 3456 = 0
   $$  
   Divide through by $$8$$:  
   $$
   x^2 + 6x - 432 = 0
   $$

5. **Solve Quadratic Equation:**  
   Factorize:  
   $$
   (x - 18)(x + 24) = 0
   $$  
   Solve for $$x$$:  
   $$
   x = 18 \, 	ext{or} \, x = -24
   $$

6. **Select Valid Solution:**  
   Since speed cannot be negative, $$x = 18$$ km/hour is the valid solution.

---

### Final Answer:  
The speed of the slower ship is **18 km/hour**, and the correct answer is **B)**.

Answer

Answer

Answer