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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?

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30 Aug 2015, 11:05

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By 4:30, Train C would have travelled 20 Kms in 30 mins or by the time Train D started. 120 Kms are left for the trains to meet. Since both trains are travelling in opposite directions, their speed becomes 60 mph. Thus they would meet in 2 hours after the Train D starts. Hence, both trains meet at 6:30.

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30 Aug 2015, 11:56

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For Train C: Speed = 40 miles/hr Distance traveled in 1/2 hr. (before train D starts) = 20 miles Since both the trains are moving in same direction Relative Speed = 40+20 = 60 miles/hr Distance to be covered = 140-20=120 miles => Time taken = 2 hrs after train D starts,i.e., 6:30 (D)
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Re: City A and City B are 140 miles apart. Train C departs City A, headin [#permalink]

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31 Aug 2015, 00:59

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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
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Re: City A and City B are 140 miles apart. Train C departs City A, headin [#permalink]

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31 Aug 2015, 06:08

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Bunuel wrote:

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

Kudos for a correct solution.

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.
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Re: City A and City B are 140 miles apart. Train C departs City A, headin [#permalink]

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31 Aug 2015, 08:20

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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

City A and City B are 140 miles apart. Train C departs City A, headin [#permalink]

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31 Aug 2015, 16:21

Bunuel wrote:

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

Kudos for a correct solution.

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

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?

* 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.
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Re: City A and City B are 140 miles apart. Train C departs City A, headin [#permalink]

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01 Jan 2018, 09:04

Bunuel wrote:

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

Kudos for a correct solution.

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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