Two cars left, at 8 am, from the same point, one traveling east at 50 mph and the other travelling south at 60 mph. At what time will they be 300 miles apart?

• As I think,
  they will 10 miles apart in 1 hr,because when a covers 50 miles in 1 hr, B covers 60 miles so B is 10 miles apart from A in 1 hr.
  Therefore 10 miles - 1 hr
  300 miles - x hr
  Solving this: 10 x = 300 => x=30 hr.So It takes 30 hr from 8 AM.
• 10 years agoHelpfull: Yes(1) No(2)
• The two cars are traveling in directions that are at right angle. Let x and y be the distances traveled by the two cars in t hours. Hence
  
  x = 50 t and y = 60 t
  
  Since the two directions are at right angle, Pythagora's theorem can used to find distance D between the two cars as follows:
  
  D = sqrt ( x 2 + y 2 )
  
  We now find the time at which D = 300 miles by solving
  
  sqrt ( x 2 + y 2 ) = 300
  
  Square both sides and substitute x and y by 50 t and 60 t respectively to obtain the equation
  
  (50 t) 2 + (60 t) 2 = 300 2
  
  Solve the above equations to obtain
  
  t = 3.84 hours (rounded to two decimal places) or 3 hours and 51 minutes (to the nearest minute)
  
  The two cars will 300 miles apart at
  
  8 + 3 h 51' = 11:51 am.
• 7 years agoHelpfull: Yes(0) No(0)