SOLUTION: Two trains going in opposite directions leave at the same thime. One train travels 15mph faster than the other train. The slower train went 270 miles in the same amount of time tha

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Two trains going in opposite directions leave at the same thime. One train travels 15mph faster than the other train. The slower train went 270 miles in the same amount of time tha      Log On


   

Question 232405: Two trains going in opposite directions leave at the same thime. One train travels 15mph faster than the other train. The slower train went 270 miles in the same amount of time that the faster train went 360 miles. Find the speed of each.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When things are traveling in opposite directions
you can combine speeds, distances and times as if
it was just one thing moving at their combined speed
given:
d+=+270+%2B+360
d+=+630 mi/hr
v%5B1%5D+=+v%5B2%5D+%2B+15
Combined speed is v+%2B+v+%2B+15+=+2v+%2B+15 (calling V%5B2%5D+=+v
--------------------
630+=+%282v+%2B+15%29%2At
630+=+2vt+%2B+15t
Note that vt is the slower trains distance vt+=+270
630+=+2%2A270+%2B+15t
630+=+540+%2B+15t
15t+=+90
t+=+6 hrs
The speed of the faster train is:
360%2F6+=+60 mi/hr
The slower tain's speed is:
270%2F6+=+45 mi/hr
check answer:
630+=+%282v+%2B+15%29%2At
630+=+%282%2A45+%2B+15%29%2A6
630+=+105%2A6
630+=+630
OK