Two trains are traveling at approximately 164 mph towards a station. Train A is traveling south and is 240 miles from the station while train B is traveling west and is 320 miles from the station. To the nearest integer, how fast is the distance between the two trains changing at this time? Reduce your answer by a factor of 10.
Could someone please help me with the set up of this problem? Thanks!
The equation you should start off with is (a^2)+(b^2)=(c^2). The a is 240 and the b is 320. Use Pythagorean Theorem to solve for what c is. Then take the derivative of the equation. You should get 2aa'+2bb'=2cc'. a' and b' are both -164 since the distance is decreasing at that rate as they approach the station. Plug in your numbers and solve for c' to get the rate that the distance between the two trains is changing.
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