How many hours would it take for a passenger train traveling 60 mph to catch a freight train traveling 40 mph if the freight train left the same depot 4 hours earlier than the passenger train?
Answer
1. What do you know?
- Speed of the two trains
- Left the same depot, so if they have to meet to pass each other they must be going the same direction
- Also, at the time they meet they have to be the same distance from the starting point
- The freight train has been on the tracks 4 hours longer than the passenger train
- Distance = Rate X time
2. You can make the following set up to diagram:
| Distance | Rate | Time | |
| Freight | 40(t + 4) | 40 mph | t +4 |
| Passenger | 60t | 60 mph | t |
(since D = R x T multiply RxT and put it in the Distance column for each train)
3. Since the distances have to be the same, set them equal to each other and solve for time.
- 40(t + 4) = 60t
- 40t + 160 = 60t (distribute the 40)
- 160 = 20t (subtract 40t from both sides of the equation)
- 8 hours = t (divide by 20 on both sides to finish solving for t)