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# An express train traveled at an average speed of 100 kilometers per

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Joined: 02 Sep 2009
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An express train traveled at an average speed of 100 kilometers per  [#permalink]

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31 Jan 2018, 23:40
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Difficulty:

55% (hard)

Question Stats:

67% (03:18) correct 33% (03:08) wrong based on 73 sessions

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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 per hour, 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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An express train traveled at an average speed of 100 kilometers per  [#permalink]

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01 Feb 2018, 01:12
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Bunuel 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 per hour, 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

Express train travel an average speed of 100 km/hour, taking the train 45 minutes to travel 75 km.
It will take the express train $$\frac{600}{75} = 8*45$$ minutes per stretch of 75 km = 360 minutes

Additionally, it stops 3 minutes after it has traveled 75 km. This would add another 21 minutes
(7 times in total - after 75,150,225,300,375,450, and 525 km) to the total time spent to travel 600 km.

The time taken by the express train to travel 600 km is 381(360+21) minutes

We have been asked to find the distance covered by the local train in this time, provided it stops
a minute after traveling 25 kms(which will take it half an hour to travel at an average of 50 km/hr)

The time taken for the local train to travel 25 km is 31 minutes.

The total distance traveled by the local train is $$\frac{381}{31}*25 = 307.5$$(approximately) (Option C)
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Re: An express train traveled at an average speed of 100 kilometers per  [#permalink]

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01 Feb 2018, 05:18

Yes the express train traveled 381 minutes in total

It takes local train 30 minutes to travel 25 kms

To travel 300 km the local train needs 360 minutes and 11 minutes. Because in 300 km it stops 11 times

Local train spends 371 minutes out of 381 minutes to travel 300 km

Therefore it has extra 10 minutes to travel 10*50/60 = 8.33

So it traveled 308.33 km
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Re: An express train traveled at an average speed of 100 kilometers per  [#permalink]

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01 Feb 2018, 09:10
Bunuel 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 per hour, 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

Express train 600/75 = 8 *3 =24 hence Express train spent 24 minutes for all stops before it did 600 km. it means that it took express train 6 hours and 24 minutes to do 600 km.

Local train 600/25 = 24 min = 24 stops. 50 *6 = 300 km

since both trains spent 24 minutes on stops, these timings cancel out, so we are left with answer A

300 km did local train.
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Re: An express train traveled at an average speed of 100 kilometers per  [#permalink]

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01 Feb 2018, 09:16
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dave13 wrote:
Bunuel 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 per hour, 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

Express train 600/75 = 8 *3 =24 hence Express train spent 24 minutes for all stops before it did 600 km. it means that it took express train 6 hours and 24 minutes to do 600 km.

Local train 600/25 = 24 min = 24 stops. 50 *6 = 300 km

since both trains spent 24 minutes on stops, these timings cancel out, so we are left with answer A

300 km did local train.

Hi dave13

The express train spends 21 minutes on stops(after 75,150,225,300,375,450, and 525 km)
However, the local train does not complete its journey along with the express train.

Hence, we can't clearly mention that the local train also spends the same time on stoppages

That's why I think the answer must be Option C and not A.
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Re: An express train traveled at an average speed of 100 kilometers per  [#permalink]

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02 Feb 2018, 11:16
1
1
Bunuel 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 per hour, 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

We are given that the express train traveled at an average speed of 100 kilometers per hour, stopping for 3 minutes after every 75 kilometers.

Let’s determine how many intervals of 75 km are in 600 km.

600/75 = 8

Since on the 8th interval the train will have stopped, the express train stopped for 3 x 7 = 21 minutes during the trip.

We also see that, without stopping, it takes the express train 6 hours to travel 600 km.

Thus, the total time spent by the express train was 6 hours and 21 minutes.

For the local train, we need to figure out how many minutes were spent on stopping in 6 hours and 21 minutes. Since the local train’s speed is 50 kmph and it travels every 25 km before it stops, it travels every 30 minutes before it stops. In 6 hours (ignoring the 21 minutes first), there are 12 intervals of 30 minutes and 11 stoppings of 1 minute, thus making a total of 6 hours and 11 minutes.

We see that we still have 10 minutes left to make up the 6 hours and 21 minutes. In these 10 minutes, the local train will stop for 1 minute first (after the 12th interval of 30-minute traveling) and then travels for 9 more minutes. Thus the actual travelling time of the local train (the time it’s moving) is 6 hours and 9 minutes, and during this time, it has traveled:

6 x 50 + 9/60 x 50 = 300 + 7.5 = 307.5 miles

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Re: An express train traveled at an average speed of 100 kilometers per &nbs [#permalink] 02 Feb 2018, 11:16
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