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# Two trains fast and slow are going from city A to city B

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Intern
Joined: 14 Feb 2019
Posts: 2
Two trains fast and slow are going from city A to city B  [#permalink]

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14 Feb 2019, 15:10
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Difficulty:

55% (hard)

Question Stats:

54% (02:59) correct 46% (02:37) wrong based on 24 sessions

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Two trains fast and slow are going from city A to city B at the same time. when the fast train has covered 2/3 of the distance. the slow train is 180Km away from city B, when the fast has arrived in city B, the slow train has covered 6/7 of the distance. How long is the distance between A and B?

A- 210 km
B- 315 km
C- 420 Km
D- 490 Km
E- 560 Km

HELP!
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Joined: 24 Jun 2008
Posts: 1387
Re: Two trains fast and slow are going from city A to city B  [#permalink]

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14 Feb 2019, 15:55
2
1
When the fast train arrives at B, the slow train has covered 6/7 of the distance. So, when they travel for the same amount of time, the slow train travels 6/7 as far as the fast train, which is another way of saying that the slow train's speed is 6/7 of the fast train's speed.

If we call the total distance between the two cities "D", when the fast train has covered 2/3 of that distance, so 2D/3 miles, the slow train will only go 6/7 as far, because its speed is 6/7 of the fast train's, so the slow train will cover (6/7)(2D/3) = 4D/7 miles. But we also know that in this time, the slow train covers D - 180 miles (all but 180 miles of the total distance). So

4D/7 = D - 180
180 = 3D/7
D = 60*7 = 420
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Intern
Joined: 04 Jun 2014
Posts: 15
Re: Two trains fast and slow are going from city A to city B  [#permalink]

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14 Feb 2019, 20:27
1
Consider Fast Train as FT and Slow train as ST. Total distance as D.
We have information of two instances (consider trains started from time T=0)
1. at T1; (2/3)D covered by FT and
at T2; D covered by FT
since distance covered is proportional to time, we can say, T1/T2= ((2/3)D)/D = 2/3

2. at T1: D-180 covered by ST and
at T2: (6/7)D covered by ST
T1/T2= (D-180)/((6/7)D)

now from both equation you can calculate D and D= 420. Answer is C.
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Re: Two trains fast and slow are going from city A to city B  [#permalink]

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16 Feb 2019, 09:56
3
Always try to organize the data into a table to be clearer. now we can deduce two equations:

T1 = $$\frac{\frac{2}{3}D}{Sf}$$ = $$\frac{D-180}{Ss}$$
T2 =$$\frac{D}{Sf} = \frac{\frac{6}{7}D}{Ss}$$
from the two equations:
$$\frac{Ss}{Sf}= \frac{D-180}{\frac{2}{3}D} = \frac{\frac{6}{7}D}{D} = \frac{6}{7}$$
$$7D-(180*7) = 4D$$
$$3D = 180*7$$
$$D = 60*7 = 420$$
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Re: Two trains fast and slow are going from city A to city B   [#permalink] 16 Feb 2019, 09:56
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# Two trains fast and slow are going from city A to city B

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