SOLUTION: Two train stations, A and B, are 300km apart. Two trains leave A and B simultaneously and proceed at constant speeds to the other station. The train from A reaches station B nine h

Algebra ->  Length-and-distance -> SOLUTION: Two train stations, A and B, are 300km apart. Two trains leave A and B simultaneously and proceed at constant speeds to the other station. The train from A reaches station B nine h      Log On


   

Question 1120901: Two train stations, A and B, are 300km apart. Two trains leave A and B simultaneously and proceed at constant speeds to the other station. The train from A reaches station B nine hours after the trains have met, and the train from B reaches the station A four hours after the trains have met. Find the speed of each train.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s[A] = train A痴 speed
Let s[B] = train B痴 speed
Let t = time in hrs for them to meet
+s%5BA%5D%2At+ = distance A travels until they meet
+s%5BB%5D%2At+ = distance B travels until they meet
覧覧覧覧覧覧覧覧覧覧覧覧-
You are given that
+s%5BA%5D%2A%28+t+%2B+9+%29+=+300+
+s%5BB%5D%2A%28+t+%2B+4+%29+=+300+
+s%5BA%5D%2At+%2B+s%5BB%5D%2At+=+300+
覧覧覧覧覧覧覧-
+s%5BA%5D+=+300%2F%28+t+%2B+9+%29+
+s%5BB%5D+=+300%2F%28+t+%2B+4+%29+
覧覧覧覧覧覧覧-
+300t%2F+%28+t+%2B+9+%29+%2B+300t+%2F%28+t+%2B+4+%29+=+300+
+t%2F%28+t+%2B+9+%29+%2B+t%2F%28+t+%2B+4+%29+=+1+
multiply both sides by +%28+t+%2B+9+%29%2A%28+t+%2B+4+%29+
+t%2A%28+t+%2B+4+%29+%2B+t%2A%28+t+%2B+9+%29+=+%28+t+%2B+4+%29%2A%28+t+%2B+9+%29+
+t%5E2+%2B+4t+%2B+t%5E2+%2B+9t+=+t%5E2+%2B+4t+%2B+9t+%2B+36+
+t%5E2+=+36+
+t+=+6+
覧覧覧覧
+s%5BA%5D+=+300%2F%28+6+%2B+9+%29+
+s%5BA%5D+=+20+ km/hr
And
+s%5BB%5D+=+300%2F%28+6+%2B+4+%29+
+s%5BB%5D+=+30+ km/hr