Question 668372: Two trains are traveling north. The first train is traveling at the rate of 40mph and the 2nd train(Starts 2 hours later) is traveling at the rate of 80 mph. How long before the 2nd train over takes the 1st train?
Answer by gwendolyn(128)   (Show Source):
You can put this solution on YOUR website! Remember that d = r*t (distance is equal to rate times time).
When the second train overtakes the first, they will have traveled the exact same distance. Therefore, we can set the rate of the first train (40 mph) times the time of the first train (t) equal to the rate of the second train (80 mph) times the time of the second train (t - 2)
The second train's time is represented by t - 2 because it will have been travelling for 2 hours less than the first train when it catches up.
40t = 80(t - 2)
Now, we can distribute the 80 to the parentheses:
40t=80t-160
Then, we can subtract 80t from both sides:
-40t=-160
Finally, we divide both sides by -40
t=4
So we know that the first train will have been travelling for 4 hours before the second train overtakes it.
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