# Thread: At what time are the trains 400 miles apart?

1. ## At what time are the trains 400 miles apart?

Two trains leave the railroad station at noon. The first train travels along a straight track at 90 mph. The second train travels at 75 mph along another straight track that makes an angle of 130 degrees with the first track.

(I can't figure out how to find the length of the sites with only knowing speeds and not the distances)

I've tried using law of cosine and 90t and 75t as lengths... is this answer correct:

t=2.67 hrs ???

2. ## Re: At what time are the trains 400 miles apart?

We have this situation (point A is the station; forgive my terrible art skills):

Everything is measured from point A. Can you make any progress from here? You could use trig, or vectors, to work out $x$, as far as I can tell. $x$ refers to the time in hours.

3. ## Re: At what time are the trains 400 miles apart?

Thank you for your help. I've tried using law of cosine and 90t and 75t as lengths... is this answer correct:

t=2.67 hrs ?

4. ## Re: At what time are the trains 400 miles apart?

We'd get:

$400^2=(75x)^2+(90x)^2-2(75x)(90x)\cos{130}$

$160,000=5625x^2+8100x^2-13500x^2\cdot\cos{130}$

$160000=x^2(13725-13500\cos{130})$

Which comes out at $x^2=7.142$, making $x=2.67$, but you need to determine what $0.67$ of an hour is in order to have the time.

Edit: Corrected an arithmetic error.