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Trains A and B start simultaneously from stations 300 miles

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Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post Updated on: 16 Apr 2013, 06:59
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Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188

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Originally posted by skamal7 on 16 Apr 2013, 06:58.
Last edited by Bunuel on 16 Apr 2013, 06:59, edited 1 time in total.
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 16 Apr 2013, 06:59
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To solve problems involving trains that travel in opposite directions the first thing to do is sum their speeds.
50+40=90 m/h They will cover 300 miles (they will meet) after \(\frac{300}{90}\) hours (space=time*speed , 300=t*90)
\(\frac{300}{90}=\frac{30}{9}=\frac{27}{9}+\frac{3}{9}=3 \frac{1}{3} h\) They'll meet after 3 1/3 hours.
How many miles will A travel is 3 1/3 hours? \(50*\frac{10}{3} = \frac{500}{3} = \frac{498}{3}+\frac{1}{3}=166+\frac{1}{3}\) miles
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 16 Apr 2013, 07:18
hi,
how come your interpreting that train will meet by 300/9 hours? i a not getting it?can you explain?
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post Updated on: 16 Apr 2013, 08:32
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188


Many ways to do this problem. However, the given speeds are 50 mph and 40 mph. Had the speeds been equal, both would have covered the exact same distance = 150 miles. However, as the speed of train A is a little more than train B, it would cover a little more than 150 miles, and a safe ballparking would lead to the answer of 167 miles.This method is only possible if the options are not spaced that closely.

Another way of doing this sum is : As the trains meet, the time taken is the same and hence constant for both. Thus, Da/50 = (300-Da)/40--> Da = 1500/9 = 1500*0.11 = 165 approx.

D.
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Originally posted by mau5 on 16 Apr 2013, 07:20.
Last edited by mau5 on 16 Apr 2013, 08:32, edited 1 time in total.
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 16 Apr 2013, 07:26
Train A travels at 50 m/h, train B travels at 40 m/h. There is a distance of 300 m between them.

To find out when whey will meet there is a simple method: imagine a train that travels at a speed equal to the sum of the speed of the single trains.

In this way you obtain a train that travels at 90 m/h, and that will cover 300 miles in 300/9 hours.
300 miles will be covered by a train that travels at 50 + a train that travels at 40 in 300/9 h: the value you'll obtain is when the trains will meet.

Check this: http://gmatclub.com/blog/2010/10/%E2%80 ... -questions.
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 16 Apr 2013, 07:47
skamal7 wrote:
hi,
how come your interpreting that train will meet by 300/9 hours? i a not getting it?can you explain?

Since we know the distance (300) and the combined rate (90), we plug it into the formula:

Distance = Rate * Time
300 = 90 * Time

We can solve for the time they will meet cause we added the rate of Train A and Train B together.

So the time will be 300/90 from dividing 90 on both sides to isolate Time in the equation above.

Time will be 3.33 hours so now you can plug that in for Train A’s distance.

Distance = Rate * Time
Distance = 50 * 3.33
Distance = 166.5 or 167 according to answer choice D.
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 18 Aug 2013, 08:00
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188


Moving towards each other so relative speed is the sum of theirs rates i.e 50+40=90mph.
So time taken to meet T=D/relative speed= 300/90=>10/3
Thus A has traveled D=R*T=> 50*10/3(time they will meet)=>167 appox

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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 18 Aug 2013, 13:10
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188


300 = 50t + 40t
or, t = 10/3.

so, Sa = 500/3 = 166.6666666 = 167
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 30 Sep 2014, 01:27
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Lets say train A has travelled distance d when it met train B; it means train B has travelled distance (300-d)

Time taken by train A = time taken by train B (To meet at the crossover)

Setting up the equation

\(\frac{d}{50} = \frac{300-d}{40}\)

d = 166.666

Answer = D
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 12 Jun 2016, 12:33
5/9*300=167 miles
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 05 Aug 2016, 04:48
I did this way:
Train A Train B
50m/hr 40m/hr
100m/hr. 80m/hr
150m/hr. 120m/hr
200m/hr. 160m/hr +- 167 in between
250m/hr. 200m/hr
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 15 May 2017, 14:12
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188


This problem deals with traveling entities , or simply trains, from opposite ends- there two premises to remember for a problem of this nature (i.e vehicles traveling from opposite ends)

1). Because they both start at the same time "start simultaneously" the amount of time they will have traveled for when they meet must be the same

In other words if 50 (t) + 40 (t) = 300 - time is a fixed variable in this problem

2). The total distance traveled by both vehicles must equal the sum of the individual distances traveled by both

so if A travels 50 miles and B travels 40 miles then the total distance must be 90 miles

90 (t) = 300
t = 3 1/3

50 (3 1/3) = 167 approx
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Re: Trains A and B start simultaneously from stations 300 miles [#permalink]

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New post 16 Feb 2018, 10:44
skamal7 wrote:
Trains A and B start simultaneously from stations 300 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 50 miles per hour and 40 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?

(A) 112
(B) 133
(C) 150
(D) 167
(E) 188


We can let time of trains A and B = t and create the following equation:

50t + 40t = 300

90t = 300

t = 300/90 = 10/3 hours

So train A will have traveled 50 x 10/3= 500/3 = 166 2/3 miles by the time they passed, which is closest to the answer of 167.

Answer: D
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Re: Trains A and B start simultaneously from stations 300 miles   [#permalink] 16 Feb 2018, 10:44
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