Two cars start at the same point and speed away along the track that forms a 110° angle. If one car travels at 24 miles per hour and the other car travels at 32 miles per hour, how far apart are the cars after 30 minutes?
21 mi
22 mi
23 mi
24 mi
25 mi

Question

Two cars start at the same point and speed away along the track that forms a 110° angle. If one car travels at 24 miles per hour and the other car travels at 32 miles per hour, how far apart are the cars after 30 minutes?
21 mi
22 mi
23 mi
24 mi
25 mi

anonymous · Answer

30 minutes are 1/2 hours, so you can easily calculate how much they've travelled, than you can use the law of cosines to calculate how far apart they are.

anonymous · Answer

First, draw a picture.

|dw:1334260082925:dw|

Then calculate the distance each car has traveled individually after 30 minutes. 30 minutes is 0.5 hours so 0.5*32=16 miles and 0.5*24 is 12 miles. Then draw another picture:

|dw:1334260434304:dw|

From this, you can get two cosine equations: cos(35)=(12+x)/h and cos(70)=x/16. Solve the second equation for x and plug it into the first equation to get h. h should be 21.33 miles.