An express train traveled at an average speed of 100 : GMAT Problem Solving (PS)
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# An express train traveled at an average speed of 100

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An express train traveled at an average speed of 100 [#permalink]

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25 Nov 2007, 20:00
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An express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers. A local train traveled at an average speed of 50 kilometers, stopping for 1 minute after every 25 kilometers. If the trains began traveling at the same time, how many kilometers did the local train travel in the time it took the express train to travel 600 kilometers?

a. 300
b. 305
c. 307.5
d. 1200
e. 1236
[Reveal] Spoiler: OA
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25 Nov 2007, 20:05
ok i figured it out..just got impatient..
people can give a shot!
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25 Nov 2007, 20:13
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Time for express train to travel 600 km =

600km/100kmh = 6 hours
600km/75 = 8 (7 stops + 1 for crossing the finish line)

total time = 6 hours 21 minutes

Distance traveled by local train in 6 hours 21 minutes:

300 km in 6 hours 12 minutes (6 hours of travel, 12 stops at 1 minute each)

so how far will it go in last 9 minutes?

9/60(50) = 9(50)/60 = 450/60 = 7.5

307.5 km in 6 hours 21 minutes

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Re: An express train traveled at an average speed of 100 [#permalink]

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26 Nov 2013, 06:49
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Re: An express train traveled at an average speed of 100 [#permalink]

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28 Aug 2014, 06:38
ashkrs wrote:
An express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers. A local train traveled at an average speed of 50 kilometers, stopping for 1 minute after every 25 kilometers. If the trains began traveling at the same time, how many kilometers did the local train travel in the time it took the express train to travel 600 kilometers?

a. 300
b. 305
c. 307.5
d. 1200
e. 1236

Soln:

we can do a guess work here to get to the right answer:

Train A total time taken to cover 600 km = 6hrs + 21mins
Train B will take 50*6 should be more than 300 (to 400 max) kms (so a/d/e are gone)

so now b and C

how many stops for 50kmph in 6 hrs = 12
21- 12= 9 (odd number) ...answer should be in fraction

Hence C
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Re: An express train traveled at an average speed of 100 [#permalink]

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04 Sep 2014, 13:21
hey,

why would we count the last stop for the express train? it has already traveled 600 km the instant it gets to the last stop. therefore, shouldn't the number of 3 minute breaks be 6 rather than 7?

And thus, the express train travels 600 km in (8 intervals of 75km)*(45 minutes) + (6 stops)*(3 minutes) = 378 minutes

Then, counting the last stop of the local train, because it will need to travel some additional amount to fill the remaining time:
The time it takes the local train to travel 300km: (12 intervals of 25km)*(30 minutes) + (11 stops)*(1 minute) = 371 minutes
Which leaves 7 minutes left over-- allowing the local train to travel an additional: (7 minutes/60 minutes)*(50 km/hour) = 5.83 km

Which adds up to 12*25 + 5.83 = 305.83km traveled by the local train...
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Re: An express train traveled at an average speed of 100 [#permalink]

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04 Sep 2014, 20:43
siggarusfigs wrote:
hey,

why would we count the last stop for the express train? it has already traveled 600 km the instant it gets to the last stop. therefore, shouldn't the number of 3 minute breaks be 6 rather than 7?

And thus, the express train travels 600 km in (8 intervals of 75km)*(45 minutes) + (6 stops)*(3 minutes) = 378 minutes

Then, counting the last stop of the local train, because it will need to travel some additional amount to fill the remaining time:
The time it takes the local train to travel 300km: (12 intervals of 25km)*(30 minutes) + (11 stops)*(1 minute) = 371 minutes
Which leaves 7 minutes left over-- allowing the local train to travel an additional: (7 minutes/60 minutes)*(50 km/hour) = 5.83 km

Which adds up to 12*25 + 5.83 = 305.83km traveled by the local train...

At the end of 600 km, you have the 8th stop, not the 7th stop. That 8th stop has not been counted.
Every 75 km, one stop. So after 150 km, you would have had 2 stops. So after 300 km, you would have had 4 stops and hence after 600 kms, 8 stops.

Also, the question is a little ambiguous.
The train travels at an average speed of 100 km/hr does not specify whether the stops are a part of the time taken to calculate average speed or not. Better verbiage would be "a train runs at an average speed of 100 km/hr and then stops for 3 mins after 75 km" and so on...
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Re: An express train traveled at an average speed of 100 [#permalink]

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01 Aug 2015, 10:14
Express Train:
600 km --> 6 hours (since 100 km/h) + stops * 3 min.
stops = 600 / 75 = 8, but as it is an integer number, the last stop in km 600 is not a real
stop, so it would be 7 stops
so, time= 6 hours + 7 * 3 min. = 6 hours 21 min

Local Train:
in 6 hours, it will make 300 km (since its speed is 50 km/hour)
in 300 km it will have 300 / 25 stops = 12, 12 stops 1 min each = 12 min
we have 6 hours 12 min, but we need to calculate how many km can it make in 6 hours
21 min, so 21-12 = 9 min
if 60 min it can make 50 km, 9 min it can make 7.5 km
so, the distance is 300 + 7.5 = 307.5 km
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Re: An express train traveled at an average speed of 100 [#permalink]

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28 Mar 2016, 18:17
is there a faster way to solve this one?
my approach:
600/100 = 6 hours without stops.
600/75 = 8, so it must have had 7 stops.
6*60+3*7 = 381 minutes.

the second train travels at 50 kmh
in 360 min, it will travel 300 km.
at every 25km, there will be a stop. so while travelling 300km, it will stop 300/25 = 12 full stops. so 12 minutes.
we have 372 minutes to travel 300km. now..we need to know what distance the train will travel in the remaining 9 minutes..
50/60 = 5/6 km/min. 5/6 * 9 = 15/2 = 7.5
so..the train travelled 300+7.5=307.5 km.
Re: An express train traveled at an average speed of 100   [#permalink] 28 Mar 2016, 18:17
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# An express train traveled at an average speed of 100

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