Question 624635
Two trains run on same track and at rates 25 and 30 mph. If the slower trains starts 1 hour earlier how long will it take the for the faster train to catch up?
I can solve this problem by

Slow  25 (x+1) 
Fast  30 (x)                 25x+25=30x -------- x =5
My questions is why can’t you solve it this way

Slow 25 (x)
Fast 30 (x-1)    ----x=6  ??????????????????????????????


Your 1st method involved you making the time that the FASTER TRAIN takes to catch the slower train x, and this resulted in 5 hours. This is correct!!!


Your 2nd method is correct also. The only difference is that for the 2nd method you made the SLOWER TRAIN'S time to get to the "meeting point," x. This means that the time it took the slower train to get to the "meeting point" was 6 hours. All you need to realize now is that the time that the faster train will take to catch the slower train is (T - 1) hours, which resulted in a time of 5 (T - 1, or 6 - 1) hours. 


You just need to remember the variables that you named.


I hope it's much clearer to you now!!


Send comments and “thank-yous” to “D” at  MathMadEzy@aol.com