Question

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 6km per hour more than the other one,then the speed,in km per hour,of the slower ship is

• A. 12
• B. 18
• C. 20
• D. 24

Answer 1

The Correct Option is B

The correct answer is B:18
Let's assume the speed of the slower ship is "x" km per hour. 
Then,the speed of the faster ship would be "x+6" km per hour. 
When they met mid-ocean and started traveling in different directions,they formed a right triangle.The two-hour delay means that they have been traveling for the same amount of time. 
Using the Pythagorean theorem,we can relate the distances traveled by both ships with the distance between them: 
\((distance)^2 = (distance\space traveled \space{by}\space the\space first\space ship)^2 + (distance \space{traveled}\space by\space the \space{second}\space ship)^2\) 
\((60 km)^2=(2 hours\times{x km/h})^2+(2 hours\times(x+6) km/h)^2\) 
Solving for x: 
\(3600 = 4x^2 + 4(x + 6)^2\) 
\(3600 = 4x^2 + 4(x^2 + 12x + 36)\)
\(3600 = 8x^2 + 48x + 144\) 
Rearranging the equation: 
\(8x^2 + 48x - 3456 = 0\)
Divide the equation by 8: 
\(x^2 + 6x - 432 = 0\)
Now,we can factor or use the quadratic formula to solve for x.Factoring may not be straightforward,so let's use the quadratic formula: 
\(x = (-b ± \sqrt{\frac{(b^2 - 4ac))}{2a}}\)
Where: 
a=1 
b=6 
c=-432 
Calculating the discriminant \((b^2 - 4ac)\): 
Discriminant=\((6^2) - 4(1)(-432) = 36 + 1728 = 1764\)
Taking the square root of the discriminant: 
\(\sqrt{1764} = 42\)
Now we can apply the quadratic formula: 
\(x = \frac{(-6 ± 42)}{2(1)}\)
\(x = (\frac{36}{2}) or (\frac{-48}{2})\)
x=18 or -24 
Since speed cannot be negative, the speed of the slower ship is 18km per hour. 

Answer 2

Let the speeds of two sheep be \(x\) km/hr and \((x+6)\) km/hr.
Then distinctive covered in \(2\) hours will be \(2x\) and \((2x+12)\) km.
Apply Pythagoras Theorem,
\((2x)^2+(2x+12)^2 = 60^2\)
\(4x2+4x2+144+48x=3600\)
\(x^2+6x+18= 450\)
\(x^2+6x-432 = 0\)
On solving,
\(x = 18\) km/hr

So, the correct option is (B): \(18\)