City A and City B are 140 miles apart. Train C departs City A, headin

Train C has traveled 20 mi in the half hour before Train D has started its journey.
140-20=120
40+20 =60 mph

120 mi/ 60 mph = 2 hrs

4:30pm + 2 hrs = 6:30pm


Answer:
D. 6:30

IMO : D


Train D leaves 30 minutes after train C.
distance traveled for 30 min = 40 x .5. Thus, at 4:30, train C has traveled 20 miles.
Thus, our trains are now 120 miles apart.

Since travelling in opposite direction the relative speed = 40+20 = 60
Distance to be covered = 120 miles

Thus Time taken = 120/60 = 2hrs

Thus total time = 30 min + 2hrs = 2hr 30 min
Start time = 4:00
Thus end Time = 6:30

By 4:30, Train C has covered 20 miles.Now, distance between the 2 trains=140-20=120 miles
Relative speed=40+20=60 miles per hour
Therefore, to cover 120 miles, both trains will take 2 hours i.e 4:30 pm+2 hours=6:30 pm
Answer D

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 4:30 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?

A. 5:00
B. 5:30
C. 6:00
D. 6:30
E. 7:00
==> distance = velocity*time. in gmat math questions, remember that time flows.
in case of train C, it travels at the speed of 40mile per 1hour from 4 pm. After 30minutes in 4:30, train C moved 20 miltes and for train D is traveled 140 = 20 + 40T +20T since it travels at the opposite direction of train C. (as for the T, it's because the same time flows in the situation. in otherwords, remember that when train C and D meet the same time is flowing thus it's not a separate t1 and t2, but the same T)

120=60T, T=2 thus 2 hours have past, and since train D started traveling at 4:30, the answer is 6:30. therefore the answer is D.

By the time Train D starts , Train C has already covered 20 Km as it travelled for 30 minutes.
The distance thus left is 120 km
Relative speed = 40 + 20 = 60 Km/h
The time thus taken = 120/60 = 2 hours from 4:30
Hence 6:30

Method 1:
Relative speed

Train C leaves city A at 4:00 and train D at 4:30.
Distance travlled by train C in 30 minutes at 40 miles/hr is 20 miles.
Now remaining distance for the two train to travel is 120 miles.
As they are moving in opposite direction, their relative speed will be 60 miles/hr.
Thus time taken will be
120/60 = 2 hours
So they will meet at 6:30

Method 2:
Ratio and rate

Train C leaves city A at 4:00 and train D at 4:30.
Distance travlled by train D in 30 minutes at 40 miles/hr is 20 miles.
Now remaining distance for the two train to travel is 120 miles.
Ratio of their speed is 40 : 20 or 2 : 1
Now 120 miles has to be covered by both.
So distance covered by each will be

2x+x = 120
or 3x=120 or x =40

So train C will cover 80 miles and train D will cover 40 miles
speed of train A is 40 miles/hr. So time taken to travel 80 miles will be
80/40 = 2 hrs

same can be done by taking train D
40/20 = 2 hrs
They will meet at 6:30

Answer: D

MANHATTAN GMAT OFFICIAL SOLUTION:

Here’s what we need to do to solve the problem.

* First, we must get the trains to leave at the same time. Train D leaves 30 minutes after train C, so we must find out how far train C has traveled in that first 30 minutes. Remembering that distance equals rate x time, we know that distance = 40 x .5 (note that 30 minutes needs to be expressed in hours.) This tells us that, at 4:30, train C has traveled 20 miles. Thus, our trains are now 120 miles apart.

* At this point all we need to do is add our rates together, to get the rate at which the trains are traveling towards one another. This gives us 40 + 20 = 60 miles per hour.

* Plug into our three part formula of D = R x T: 120 = 60 x T, therefore T = 2 hours.

* If we started at 4:30 and traveled for two hours, it is now 6:30, which is the correct answer to this question.

The strategy we just employed will also work on problems in which the trains are traveling away from each other. On test day, rather than feel yourself getting anxious when you see a question that sounds similar to the “Two trains…” scenario, just take a deep breath, envision the scenario, and take it step by step.

Train C starts 30 minutes earlier than Train D,

Total Distance = 140 kms

Therefore it has covered 40*1/2 = 20 kms

So Distance remained = 140 - 20 = 120 kms

As both trains are heading towards each other, there effective speed is 40+20 = 60 kms/hr

Time taken to meet = 120 / 60 = 2 hrs + 30 minutes (As train C started 30 minutes earlier)

Meeting time of train = 4:00 + 2:30 = 6:30

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