Two trains are driving toward one another. The first train leaves Town A at 5am traveling at 60 miles per hour. The second train leaves Town B at 7am traveling at 70 miles per hour. the distance between Town A and Town B is 455 miles. What is the EXACT time that the collision will occur?
The trick with word problems is to pick them apart to see what you know, then build equations that you can solve. It takes some practice.
In this problem, we know that one train starts two hours before the other one and travels at a known rate. Let's calculate how far it goes in those two hours:
d = rt = 2 hrs * 60 mi/hr = 120 mi
The time is now 7:00 and the trains are 455 - 120 = 335 mi apart.
Now both trains are moving, one traveling at 60 mi/hr and the other at 70 mi/hr.
Their closing speed is just 60 + 70 = 130 mi/hr, and the total distance to go is 335 mi.
Solve the rate equation for t to get t = d/r. Plug in 335 for d and 130 for r.
Time to collision is t = 325 / 130 = 2.5769 hrs.
That's 2 hours with a remainder of 0.5769
0.5769 * 60 minutes = 34.615 minutes
0.615 * 60 seconds = 37 seconds
The time of collision will thus be the sum of 2 hrs + 2.5769 hrs added to the 5:00 starting time.
Tc = 5:00 + 4.5769 = 5:00 + 4:00 + 0:34 + 0:00:37 = 9:34:37
Sometimes, a problem will even ask where they would meet. Once you get to the point where you know the total travel times of both trains and their travel times, you could calculate how far each one went and find the exact location where they meet. You can treat each train's distance as a separate problem since you now know what each one did independently of the other. Try it! To check, their distances added together should be 455 when you're finished.
I hope this is helpful.