Two automobiles leave from the same point in Chicago at the same time and travel along straight highways that differ by 65o. If their speeds are 62 mi/hr and 74 mi/hr, respectively, determine how far apart the cars are after 29 minutes. Round answer to two decimal places.

Question

anonymous · Answer

65o?

anonymous · Answer

here are the options:40.76 miles
 
 B.	
 
25.48 miles
 
 C.	
 
45.86 miles
 
 D.	
 
30.57 miles
 
 E.	
 
35.66 miles

anonymous · Answer

35.66 miles is the answer.  Note that in 29 minutes the cars travel

62 x (29/60) = 29.6666667 miles

and 

74 x (29/60) = 35.76666667 miles

then using the Law of Cosines we have

c^2 = 29.67^2 + 35.77^2 - 2(29.67)(35.77)cos(65)

and taking the square root we have

c = 35.66 miles