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

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

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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An express train traveled at an average speed of 100 kilometers per [#permalink]
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Definite 3 minute question.

Key is to first determine the time taken by the express train to travel the 600 km.

Break this up into two parts:

Part 1: driving time

Express train must travel the 600 km and he does so at 100 kmph

T = (600) / (100) = 6 hours

Part 2: stopping time

Every 75 km driven, the trains stops for 3 minutes. The key here is to realize that 600 is a multiple of 75.

This means when the train reaches the 600 km mark, it does not need to stop for another 3 minutes because the train has reached its destination.

(600 km) / (every 75 km it stops) = 8 stops

8 stops - (Last stop which is in actuality the destination) = 7 stops throughout the journey of 600 km

(7 stops) * (3 min per stop) = extra +21 minutes added in which it stops

6 hours and 21 minutes = Total Time taken

Q: how much distance can the local train travel in 6 hours and 21 minutes?

We are told that every 25 km it stops for 3 minutes.

The local train’s speed:
50 km ———> each 1 hour
25 km ——-> each 30 min

This means each 30 minutes, the local train will have traveled 25 km. It will then stop for 1 minute. After the stop, it will go again another 25 km.

(1st) Stopping Time
Throughout 6 hours, there are 12 intervals of 30 minutes ——-> (6 hr) / (1/2 hr) = 12

So for the first 6 hours the local train drives ——> it makes 12 stops for 1 minute each = +12 min of stopping

(2nd)Driving Time

In these 6 hours, the local train drives a distance of: (50 kmph) * (6 hr) = 300 km

Thus far the local train has covered 300 km and used 6 hours to drive with an extra 12 min of stopping time

Out of the 6 hours and 21 minutes it has available, the local train has 9 minutes remaining to keep driving.

(50) * (9/60) = 45/6 = 7.5 km

300 + 7.5 = 307.5 km

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

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]
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]
ScottTargetTestPrep 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

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