Trains A and B are traveling in the same direction on parallel tracks...?

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Junebuge

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Train A is traveling at 40mph and train B is traveling 48mph. Train A passes a station at 2:25am. If train B passes the same station at 2:40am, at what time will train B catch up to train A?
 
Train A has a 15 minute head start on B. Using d = v*t this equates to 40 * 0.25 = 10 miles.

Because B has an 8mph advantage over A, we can use this information to find how long it would take to cover this 10 mile head start. t = d / v = 10 / 8 hours.

10 / 8 hours can be written as 1 hour 15 minutes. Add this to 2:40am and we find they meet at 3:55am
 
1) Difference in timing of passing the same station is = 2:40 - 2:25 = 0:15 = 1/4 hour

2) Let the two trains meet at a distance of x miles from this station.

3) Time taken by train A to cover this distance of x km = x/40 hour and that by train B = x/48 hour

4) But from step (1), since there is a difference of 1/4 hour between them at the initial station,

==> x/40 = x/48 + 1/4

==> x/40 - x/48 = 1/4

==> 6x - 5x = 60 [Multiplying both sides by 240, which is the LCM of 4, 40 and 48]

So x = 60 miles

Time taken to cover this 60 km by train A = 60/40 = 1.5 hour = 1 hr + 30 min

Hence train B catches the train A at 2:25 + 1:30 = 3:55 am
 
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