A Train Left A Station P at 6 am and Reached Another Station Q at 11 GMAT Problem Solving

Question: A train left a station P at 6 am and reached another station Q at 11 am. Another train left station Q at 7 am and reached P at 10 am. At what time did the two trains pass one another?

1. 7:50 am
2. 8:13 am
3. 8:30 am
4. 8:42 am
5. 9:03 am

Answer:
Approach Solution (1):
Let the distance between the two stations be 150 kms
Time taken by Train A = 5 hrs
Speed of Train A = 30 km/h
Time taken by Train B = 3 hrs
Speed of Train A = 50 km/h
Since they are travelling in opposite direction, their relative speed = 30 + 50 = 80
They must have passed one another at 120 / 80 = 1.5 hours past 7 am = 8:30 am
Time taken by Train A = 5 hrs
Speed of Train A = 30 km/h
Correct option: C

Approach Solution (2):
Let’s call the train leaving P station is T1 and that leaving Q station is T2
Choose a number to be distance between P and Q, let’s say 15 (miles)
S1 = S2 = 15
It took the train T1 5 hours (6 am – 11 am) to travel: T1 = 5
It took the train T2 3 hours (7 am – 10 am) to travel: T2 = 3
Formula: s = t * v
Speed of T1: v1 = S1 / T1 = 3 (miles/hour)
Speed of T2: v2 = S2 / T2 = 5 (miles/hour)
At 7 am, train T1 already traveled: 1 * 3 = 3 (miles)
At that time, the distance between 2 trains is: s = 15 – 3 = 12 (miles)
Because 2 trains take opposite directions: s = t (v1 + v2)
Therefore, the number of hours it would take for both the trains to pass one another is: t = S / (v1 + v2) = 12 / (3 + 5) = 1.5 (hours)
1.5 hours since 7 am = 8:30 am
Correct option: C

Approach Solution (3):
Let the distance be D
Speed of the first train be X
Speed of the second train be Y
Time taken by first train = 5 hours
Time taken by second train = 3 hours
\(x = {D\over5} and Y = {D\over3}\)
First train travel for 1 hour from 6 to 7 am so distance covered is D – X * 1 =\(D-{D\over5}=4*{D\over5}\)
Now using concept of relative velocity we have:
Time to meet = Distance traveled / Relative velocity
Relative velocity =\({D\over5}+{D\over3}\)as trains are travelling in opposite direction
So we have\(\frac{4*{D\over5}}{({D\over5}+{D\over3})}=\frac{4\over5}{8\over15}={3\over2}=1.5\)hours
So the train will meet at 8:30 am
Correct option: C

“A train left a station P at 6 am and reached another station Q at 11 am. Another train left station Q at 7 am and reached P at 10 am. At what time did the two trains pass one another?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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