Trains M and N are traveling west on parallel tracks. At exactly noon, the front of train M, which is...
GMAT Two Part Analysis : (TPA) Questions
Trains M and N are traveling west on parallel tracks. At exactly noon, the front of train M, which is traveling at a constant speed of \(\mathrm{80 \text{ km/h}}\), is at rail crossing at location X, and the front of Train N, which is traveling at a constant speed of \(\mathrm{65 \text{ km/h}}\), is \(\mathrm{30 \text{ km}}\) west of the rail crossing at location X. The trains continue traveling at their respective speeds until the front of Train M and the from of Train N are simultaneously at the rail crossing at Location Y.
In the table, identify the number of kilometers that the front of Train M has traveled between noon and 12:45 p.m. and the number of kilometers that the front of Train N has traveled between noon and 1:00 p.m.
Phase 1: Owning the Dataset
Let's draw a timeline showing the trains' positions:
At noon (12:00):
Location X
|-------- 30 km -------->
M N
↓ ↓
(80 km/h west) (65 km/h west)
Given information:
- Train M: Starts at location X, travels west at 80 km/h
- Train N: Starts 30 km west of X, travels west at 65 km/h
- Both trains eventually meet at location Y
Phase 2: Understanding the Question
We need to find:
- Distance Train M travels from noon to 12:45 p.m.
- Distance Train N travels from noon to 1:00 p.m.
This is a direct application of: \(\mathrm{Distance} = \mathrm{Speed} \times \mathrm{Time}\)
Phase 3: Finding the Answer
For Train M (noon to 12:45 p.m.):
- Time elapsed: 12:45 - 12:00 = 45 minutes = 0.75 hours
- Speed: 80 km/h
- Distance = \(80 \times 0.75 = 60\) km
For Train N (noon to 1:00 p.m.):
- Time elapsed: 1:00 - 12:00 = 1 hour
- Speed: 65 km/h
- Distance = \(65 \times 1 = 65\) km
Phase 4: Solution
Final Answer:
- Front of Train M: 60 km
- Front of Train N: 65 km
Both calculations directly apply the distance formula to find how far each train travels in the given time period.