Last visit was: 17 Jul 2024, 06:34 It is currently 17 Jul 2024, 06:34
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94372
Own Kudos [?]: 641636 [12]
Given Kudos: 85676
CEO
Joined: 26 Feb 2016
Posts: 2865
Own Kudos [?]: 5319 [5]
Given Kudos: 47
Location: India
GPA: 3.12
Intern
Joined: 05 Mar 2015
Posts: 26
Own Kudos [?]: 18 [0]
Given Kudos: 111
Location: Azerbaijan
GMAT 1: 530 Q42 V21
GMAT 2: 600 Q42 V31
GMAT 3: 700 Q47 V38
VP
Joined: 09 Mar 2016
Posts: 1142
Own Kudos [?]: 1026 [0]
Given Kudos: 3851
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.
CEO
Joined: 26 Feb 2016
Posts: 2865
Own Kudos [?]: 5319 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Re: An express train traveled at an average speed of 100 kilometers per [#permalink]
1
Kudos
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.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19148
Own Kudos [?]: 22654 [3]
Given Kudos: 286
Location: United States (CA)
Re: An express train traveled at an average speed of 100 kilometers per [#permalink]
1
Kudos
2
Bookmarks
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

VP
Joined: 10 Jul 2019
Posts: 1385
Own Kudos [?]: 577 [1]
Given Kudos: 1656
An express train traveled at an average speed of 100 kilometers per [#permalink]
1
Kudos
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

Posted from my mobile device
Non-Human User
Joined: 09 Sep 2013
Posts: 33998
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: An express train traveled at an average speed of 100 kilometers per [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: An express train traveled at an average speed of 100 kilometers per [#permalink]
Moderator:
Math Expert
94372 posts