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Difficult Math Problem #16

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800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Problem #16

Post Mon Sep 18, 2006 7:54 pm
OA coming after a few people answer..

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

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gamemaster Senior | Next Rank: 100 Posts Default Avatar
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Post Wed Sep 20, 2006 6:44 am
clarification:

381/31 = 12 and a reminder of 9 (which are 9 minutes)

the local train drives at 50km/h so in 9 minutes it will pass:

(9/60)*50 = 7.5 km

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800guy Master | Next Rank: 500 Posts Default Avatar
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Post Wed Sep 20, 2006 4:57 pm
OA:

the answer is C: 307.5 km
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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gamemaster Senior | Next Rank: 100 Posts Default Avatar
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Post Wed Sep 20, 2006 6:44 am
clarification:

381/31 = 12 and a reminder of 9 (which are 9 minutes)

the local train drives at 50km/h so in 9 minutes it will pass:

(9/60)*50 = 7.5 km

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800guy Master | Next Rank: 500 Posts Default Avatar
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Post Wed Sep 20, 2006 4:57 pm
OA:

the answer is C: 307.5 km
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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saurabhc Newbie | Next Rank: 10 Posts Default Avatar
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Post Tue Sep 19, 2006 6:43 am
600/75 = 8 so the train in all had to come across 7 stations by the last 8th station it covered the 600 kilometers so no halting time.

7stations * 3mins = 21 mins THe total time the train halted

75 kms it covers in 45 mins , which is the journey for 1 station
so in all 45 *8 = 360 mins

In all time 360 +21 = 381

For local train,
50kmph so it travels 25 kmph in 30 mins + a 1 min break
so in 31 mins it travels 25 km

mins - km
31 - 25
381 - x

so x= 381*25/31= ~ 307[Anyone knows a better way to calculate this]

OR a better way to solve this. Btw Ans C

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gamemaster Senior | Next Rank: 100 Posts Default Avatar
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Post Tue Sep 19, 2006 4:09 am
i ment 382/31 = 12 + 9 min

and (9/60)*50 = 7.5

so the answer is indeed: 307.5

final post from me on this thread Smile

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