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Difficult Math Problem #16

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Difficult Math Problem #16

by 800guy » 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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solution

by gamemaster » Tue Sep 19, 2006 3:10 am
600 = 8 * 75

so there were 7 stopps of 3 minutes and 8 rides that took (75/100)*60 = 45 min

total jurney was 8*45+21 = 381 min

the local train takes 30min to pass 25Km + 1minute

so 381/31 = 12*31 + 8 minute

so the local train would pass 12*25 + (8/60)*50 =~ 306.6

* if i would add to this 3 minute, i would get 307.5, but i think the accurate answer is 300.666

so: C
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...

by gamemaster » Tue Sep 19, 2006 3:11 am
i ment 306.666 ...
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by gamemaster » 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 :)
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by saurabhc » 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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.

by gamemaster » 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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by 800guy » 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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