<PRE><B>Question 624635</B>
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
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My questions is why can’t you solve it this way

Slow 25 (x)
Fast 30 (x-1)    ----x=6  ??????????????????????????????
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Multiplying x-1 times 30 gives a headstart of 30 miles, not 25.
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Do it like this.
The 1st train is 25 miles away when the 2nd starts.
The 2nd gains in the 1st at 5 mi/hr (a better statement is the speed of the 2nd wrt to the 1st is 5 mi/hr, since all motion is relative)
25/5 = 5 hours.
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