A train left a station P at 6 am and reached another station Q at 11

Let the distance between the stations be x

First train(A) left station P- 6 AM and reached station Q - 11 AM, Time taken :5 hours.
Second train(B) left the station Q - 7 AM and reached station P - 10 AM, Time taken : 3 hours

Also since one of the trains left an hour later, the other train would have
traveled for an hour, covering \(\frac{x}{5}\) of the distance(Since Time: 5 hours)

For the remaining \(\frac{4x}{5}\) of the distance, the trains, together travel a distance of \(\frac{x}{3} + \frac{x}{5}(\frac{8x}{15})\) in an hour
Time taken for the trains to meet is \((\frac{4x}{5}/\frac{8x}{15}) = \frac{4*15}{5*8}= \frac{3}{2} hours\)

The trains meet at 8:30 am(Option C), one and an half hours after train B leaves the station Q.

Imo C
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/5 and Y=D/3
first train travel for 1 hour from 6 to 7 am so distance covered is D-X*1=D-D/5=4*D/5
Now using concept of relative velocity we have
Time to meet =Distance traveled/Relative velocity
Relative velocity =D/5+D/3 as the trains are travelling in opposite direction
So we have (4*D/5)/(D/5+D/3) =(4/5)/(8/15)=3/2=1.5 hours
so the trains will meet at 8.30 am

As per the explanation here the first train starts at 6 AM i.e. 1 hour before the other train started journey. so the first train has already travelled 30 km till 7 AM wgen second train starts moving

hence, at 7 AM the distance left between two trains = 150-30 = 120
Relative speed at 7 AM = 30+50 = 80 km/h

Time = 120/80 = 1.5 hours


Hope this helps!!!

Let the distance between P and Q be 'd' miles and the time taken by T1 (which left P at 6:am) to travel to the point it meets T2 be 't' hrs.
T/4, distances covered by T1 and T2 until they meet is t(d/5)* miles and (t-1)**(d/3)* respectively. Obviously, the sum of these two distances is 'd'. Thus, t(d/5)+(t-1)(d/3)=d. So, t=2.5 hrs. Thus, T1 meets T2 2.5 hrs after it departs St.P, i.e at 8:30 am.

*Times taken by T1 and T2 to cover 'd' miles is 5 hrs and 3 hrs so their speeds are d/5 mph and d/3 mph respectively.
**T2 starts 1 hr after T1 so it travels 1 hr less.

Let's call the trains A and B. Note that both trains travel the same distance. (We'll get to that)

Train A's total time = 5 hours
Train B's total time = 3 hours

Let's choose an easy LCM between the two for distance. Let distance = 15 miles

Thus:
Train A's speed = 15/5 = 3 mph
Train B's speed = 15/3 = 5 mph

Now we know their speed! The question now asks when they meet up. Let's make a quick timetable for the time vs. distance travelled at each 1 hour interval: (We want their distances to match up!)

@ 6AM: Train A --> 0 miles || Train B --> 0 miles
@ 7AM: Train A --> 3 miles || Train B --> 0 miles
@ 8AM: Train A --> 6 miles || Train B --> 5 miles
@ 9AM: Train A --> 9 miles || Train B --> 10 miles

Oh! So we know they cross somewhere between 8AM and 9AM. Let's choose something in between:

@830AM: Train A --> 7.5 miles || Train B --> 7.5miles [notice it's halfway between 8AM and 9AM bc of constant speed]

--> this is where they meet! 830AM --> C is your correct answer

C

The ratio of speeds is 3:5 as the ratio of the time taken is 5:3.
Let's choose a distance that's divisively by both 3 and 5, say 300.

Speeds of the train are now 60 and 100.
Train at P had covered 60kms when The train at Q started.
After another hour, train P is at 120 km mark, while the other is at 200 mark. After another hour, at 180 Nd 100, so already crossed.
So, after 30 mins, they both at 150 mark.

P(5hrs) R Q(3hrs)
|---------|---------------|
R - meeting point
p-q distance=D
v(p)=D/5,v(q)=D/3
Since P already started and traveled 1 hr when Q started
P traveled D/5 in one hour ..
Distance between them is now D-D/5=4D/5
New distance
P(5hrs) R Q(3hrs)
|----x-----|------(4d/5)-x---------|
They will reach R at same time.

so t1=t2,d1/v1=d2/v2
x/(D/5)=(4D/5-x)/(D/3)
x=3D/10
t=D/v=(3D/10)/(D/5)=1.5(1 hour 30 mins)
Total time =1+1.3=2.30
Time=6+2.30=8.30

at 8:00 am, train 1 has covered 2/5 of the distance
while train 2 has covered 1/3 of the distance
thus, 4/15 of the distance remains
4/15 distance/(1/5+1/3) combined rate=1/2 hour
8:00 am+1/2 hour=8:30 am
C

I think the question should say that the trains are traveling at constant speeds.

We’re given information in which both trains cover the same distance.

Given the same constant distance, the Ratio of time traveled is inversely Proportional to the Ratio of Speeds



Time for train 1 from P : Time for train 2 from Q = 5 hours : 3 hours

Speed for train 1 : Speed for Train 2 = 3 : 5

Let train 1 leaving from P have a Speed = 3 mph

Distance from P to Q = (3 mph) * (5 hours to reach destination) = 15 m

Train 1 gets a 1 hour headstart when it leaves at 6 AM. 3 miles of the Gap Distance is closed.

At 7 AM ——-> 12 miles is between the 2 trains

Since train 1 Speed = 3 mph

Train 2 speed = 5 mph

Time to meet = (Gap Distance) / (Speed of 1 + Speed of 2)

Time = 12 / (3 + 5) = 12/8 = 3/2 hours

The trains will meet 1.5 hours after 7 AM

Answer: 8:30 AM

Posted from my mobile device

Shouldn't the last step be 150/80. Instead of 120/80..since we are assuming distance as 150 ~1.5 hrs?

Posted from my mobile device

Given: 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.

Asked: At what time did the two trains pass one another?

Let the distance between P & Q be D km.

P-Q:-
Time = 5 hours
Speed = D/5 kmh

Q-P:-
Time = 3 hours
Speed = D/3 kmh

From 6-7 am
First train travelled = D/5 km

Remaining Distance = D - D/5 = 4D/5 km
Relative speed = D/3 + D/5 = 8D/15
Time taken = (4D/5)/(8D/15) = 4*15/5*8 = 3/2 = 1.5 hours

Time when they meet = 7 + 1.5 = 8.5 hours = 8:30 am

IMO C

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.