SOLUTION: I'm not exactly sure what category this question belongs in, but here it is: A train leaves Smithville and travels south at a speed of 60 mph. Three hours later, a second train

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I'm not exactly sure what category this question belongs in, but here it is: A train leaves Smithville and travels south at a speed of 60 mph. Three hours later, a second train       Log On


   

Question 33683: I'm not exactly sure what category this question belongs in, but here it is:
A train leaves Smithville and travels south at a speed of 60 mph. Three hours later, a second train leaves on a parallel track and travels south at a speed of 90 mph. How far from the station will the second train overtake the first train?
Answer by mukhopadhyay(490) About Me  (Show Source):
You can put this solution on YOUR website!
Assume t hours be the time it would take the second train to overtake the first.
Second train travelled for t hours before passing the first;
The first train left three hours earlier, so it travlled for (t+3) hours before the second train passed it.
First train travels at 60 mph
=> The first train travelled (t+3)60 miles in (t+3) hours;
Similarly, the second train travlled 90t miles in t hours;
Distance travelled by the first train in (t+3) hours = Distance travelled by the second train in t hours (because one passed another and they started from the same place);
(t+3)60 = 90t
=> 2(t+3) = 3t
=> t = 6
It took 6 hours for the second train to pass the first train ;
Distance travelled by second train in 6 hours = 90*6 = 540 miles.
Answer: The second train will overtake the first train 540 miles from the station.