We can set up a distance equation based on the information given.
Let t be the amount of time it takes for the second train to catch up to the first train in hours.
The distance the slower train traveled is given by 50x, where x is the time it takes for the slower train to travel.
The distance the faster train traveled is given by 55(x - 0.5), where x - 0.5 represents the time it takes for the faster train to travel, since it left 30 minutes after the slower train.
Since the two trains have traveled the same distance when they meet, we can set up the equation:
50x = 55(x - 0.5)
Now, we can solve for x:
50x = 55x - 27.5
-5x = -27.5
x = 5.5
Since x represents the time it takes for the slower train to travel, it took 5.5 hours for the slower train to travel.
The second train caught up to the first train 30 minutes after it left the station, so the total time it took for the second train to catch up to the first train is 5.5 + 0.5 = 6 hours.
Therefore, the second train overtook the first train 6 hours after the first train left the station.
A train traveling 50 mph left a station 30 minutes before a second train running at 55 mph. How soon did the second train overtake the first?
If 50x represents the distance the slower train travels, then the faster train travels
55(x + 0.5)
50 + 30x
55(x - 0.5)
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