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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] New post 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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 [#permalink] New post 25 Nov 2007, 20:05
ok i figured it out..just got impatient..
people can give a shot!
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 [#permalink] New post 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

Answer: C
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Re: An express train traveled at an average speed of 100 [#permalink] New post 26 Nov 2013, 06:49
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Re: An express train traveled at an average speed of 100 [#permalink] New post 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] New post 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] New post 04 Sep 2014, 20:43
Expert's post
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] 04 Sep 2014, 20:43
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