SOLUTION: Two ships meet, one going off to the south and the other, to the west. Two hours after their encounter, they are 60 km apart. Find the speed of each ship, if it is known that the s

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Question 1196179: Two ships meet, one going off to the south and the other, to the west. Two hours after their encounter, they are 60 km apart. Find the speed of each ship, if it is known that the speed of one of them is 6 km/h greater than that of the other.
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.
Two ships meet, one going off to the south and the other, to the west.
Two hours after their encounter, they are 60 km apart.
Find the speed of each ship, if it is known that the speed of one of them is
6 km/h greater than that of the other.
~~~~~~~~~~~~~~~ 

Let x be the speed of the slower ship, in kilometers per hour.

Then the speed of the other ship is (x+6) km/h.


You have a right angled triangle with the legs 2x and 2(x+6) kilometers
and the hypotenuse of 60 kilometers.


Write the Pythagorean equation

    (2x)^2 + (2(x+6))^2 = 60^2

    4x^2 + 4*(x+6)^2 = 3600

     x^2 + (x+6)^2 = 900

     2x^2 + 12x + 36 = 900
   
      x^2 + 6x - 432 = 0.


Using the quadratic formula, find the solutions of the equation. They are 18 and -24.


Keep the positive solution and reject the negative one.


ANSWER.  The slower ship speed is 18 km/h; the faster ship speed is 18+6 = 24 km/h.

Solved.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Two ships meet, one going off to the south and the other, to the west. Two hours after their encounter, they are 60 km apart. Find the speed of each ship, if it is known that the speed of one of them is 6 km/h greater than that of the other.
---------------
r = speed of slower ship
r^2 + (r+6)^2 = (60/2)^2 = 900
r^2 + r^2+12r + 36 = 900
2r^2 + 12r - 864 = 0
r^2 + 6r - 432 = 0
(r + 24)*(r - 18) = 0
r = 18 km/hr
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