Two buses are travelling on the highway from X to Y . : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 13:53

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Two buses are travelling on the highway from X to Y .

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 10 Apr 2012
Posts: 276
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 5

Kudos [?]: 733 [0], given: 325

Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

24 Jun 2013, 13:15
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

62% (04:06) correct 38% (02:56) wrong based on 117 sessions

HideShow timer Statistics

Two buses are travelling on the highway from X to Y . The speed of the first bus is 60KMPH and the second bus travels at the speed of 40KMPH. The first bus leaves at 11 AM and the second leaves 15 mins later. The first bus starts back for X, 15 mins after it reaches Y . How far from Y will the first Bus meet the second ?Also, after how much time will they meet each other after the departure of the first bus from X , if the distance between X and Y is 180 KM.

A)36 KM , 3 Hrs 36 Mins
B)36 KM, 3 Hrs 51 Mins
c)24KM, 3 Hrs 50 mins
d)24 KM, 3 hrs 51 mins
e)48 KM, 2 Hrs 51 mins
[Reveal] Spoiler: OA
Manager
Joined: 09 Apr 2013
Posts: 214
Location: United States
Concentration: Finance, Economics
GMAT 1: 710 Q44 V44
GMAT 2: 740 Q48 V44
GPA: 3.1
WE: Sales (Mutual Funds and Brokerage)
Followers: 4

Kudos [?]: 77 [0], given: 40

Re: Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

24 Jun 2013, 15:50
This problem is best to do in steps, since you have to find out how far the buses go and then come back... you could do the math into one, giant equation but it's easier to segment it out and draw a timeline, especially since we don't have a calculator. .

So it takes the first bus $$\frac{180km}{60mph} = 3:00 hours$$ to get to point Y. It then waits there another 15 minutes...

The second bus waits 15 minutes and then starts heading for y at $$40mph$$

this means that at the time the first bus leaves point Y, the second bus will have been travelling for 3:00 hours $$(3:15-15)$$

Which means that it will have covered $$40mph * 3:00 hours = 120m$$

Which means that they are now 3:15 into the journey and $$180m - 120m =60m$$ apart...

The two of them, together, can close the distance in $$\frac{60m}{(40mph + 60mph)} = .6 hours = 36 minutes$$

So the total time before they meet is $$3:15 + 36= 3:51minutes$$

The total distance away from point X of the second bus would be $$120m + (40mph * .6hours) = 144 miles$$ which means that the bus has $$180-144= 36 miles$$ left to go.

So the final answer is B.
Verbal Forum Moderator
Joined: 15 Jun 2012
Posts: 1153
Location: United States
Followers: 259

Kudos [?]: 2862 [1] , given: 123

Re: Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

25 Jun 2013, 00:31
1
KUDOS
Time for 1st bus travels from X to Y = 180/60 = 3h
Time for 2nd bus travels from X to Y = 180/30 = 4.5h

Because 1st bus traveled faster ==> 1st bus must meet 2nd when 1st bus went back from Y to X

t = time 2nd bus traveled to meet 1st bus
==> 2nd bus's distant = 40t
==> 1st bus's distant = 180 + 60(t - 3 + 1/4 - 1/4) because 1st bus started 15m (1/4h) earlier than 2nd bus, but waited 15m (1/4h) before traveling back to X.

We have equation: 40t + 60(t - 3) = 180
==> t = 3.6 h = 3h and 36 minutes

Question #1: How far from Y will the first Bus meet the second?
distant from Y = 60(3.6 -3) = 36km

Question #2: how much time will they meet each other after the departure of the first bus from X?
Time = time 2nd bus traveled to meed 1st bus + 15 minutes = 3h 36minutes + 15minutes = 3h 51 minutes.

Hence, B is correct.

Hope it helps.
_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMW Chief of Design.

Last edited by Narenn on 26 Jun 2013, 08:38, edited 1 time in total.
Typo Corrected
Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 160 [0], given: 134

Re: Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

08 Aug 2013, 10:42
Two buses are travelling on the highway from X to Y . The speed of the first bus is 60KMPH and the second bus travels at the speed of 40KMPH. The first bus leaves at 11 AM and the second leaves 15 mins later. The first bus starts back for X, 15 mins after it reaches Y . How far from Y will the first Bus meet the second ?Also, after how much time will they meet each other after the departure of the first bus from X , if the distance between X and Y is 180 KM.

Round trip from X to Y to X. Distance is 180 km. Round trip = 360 km.

Bus A speed: 60 km/hour
leaves at 11:00 AM
Turns around 15 minutes after it reaches Y
Bus B speed: 40 km/hour
Leaves at 11:15 AM

Bus A reaches Y at 2:00 PM and heads back at 2:15 PM.
By the time bus A heads back, bus B has traveled for 3 hours meaning it has covered 120 km. At 2:15, bus A and bus B are 60 km apart. We can treat closing velocity as a combination of both speeds. In other words, time = distance/rate ===> time = 60/(40km/h + 60 km/h) ===> time = 60km/100km ===> time = .6 hours = 36 minutes. We know that it will take 36 minutes for B to meet A from the time when B has traveled 120 km which means that B will have traveled 3 hours + 36 minutes = 3:36 when they meet. B travels at 40 km/h so in 36 minutes it travels: distance=rate*time ===> distance = 40km/h*.6 ===> it travels an additional 24 km. B is a total of 180-120-24 = 36 km away from Y.

ANSWER: A)36 KM , 3 Hrs 36 Mins

ANSWER: A)36 KM , 3 Hrs 36 Mins

The question asks for how long will they have been traveling for after the departure of A. It takes them 3:36 to meet one another but that is the combined time of A and B. A leaves 15 minutes before B so it has traveled an additional 15 minutes before they meet: 3:36 + :15 = 3:51.

Last edited by WholeLottaLove on 08 Aug 2013, 11:16, edited 1 time in total.
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313
Followers: 107

Kudos [?]: 270 [1] , given: 66

Re: Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

08 Aug 2013, 10:51
1
KUDOS
Expert's post
WholeLottaLove wrote:
Two buses are travelling on the highway from X to Y . The speed of the first bus is 60KMPH and the second bus travels at the speed of 40KMPH. The first bus leaves at 11 AM and the second leaves 15 mins later. The first bus starts back for X, 15 mins after it reaches Y . How far from Y will the first Bus meet the second ?Also, after how much time will they meet each other after the departure of the first bus from X , if the distance between X and Y is 180 KM.

Round trip from X to Y to X. Distance is 180 km. Round trip = 360 km.

Bus A speed: 60 km/hour
leaves at 11:00 AM
Turns around 15 minutes after it reaches Y
Bus B speed: 40 km/hour
Leaves at 11:15 AM

Bus A reaches Y at 2:00 PM and heads back at 2:15 PM.
By the time bus A heads back, bus B has traveled for 3 hours meaning it has covered 120 km. At 2:15, bus A and bus B are 60 km apart. We can treat closing velocity as a combination of both speeds. In other words, time = distance/rate ===> time = 60/(40km/h + 60 km/h) ===> time = 60km/100km ===> time = .6 hours = 36 minutes. We know that it will take 36 minutes for B to meet A from the time when B has traveled 120 km which means that B will have traveled 3 hours + 36 minutes = 3:36 when they meet. B travels at 40 km/h so in 36 minutes it travels: distance=rate*time ===> distance = 40km/h*.6 ===> it travels an additional 24 km. B is a total of 180-120-24 = 36 km away from Y.

ANSWER: A)36 KM , 3 Hrs 36 Mins

Hey wholelottalove, I think you forgot to add back the 15 minutes that the bus waited at location Y. It drove for 3 hours one way and 36 minutes the other, but there was a respite of 15 minutes, hence why 3:51 and not 3:36.

On a side note, I've never seen an actual GMAT question with multiple components to solve like this one. It's a good question to solve, but it's not a real GMAT question.

Thanks!
-Ron
_________________
Senior Manager
Joined: 13 May 2013
Posts: 472
Followers: 3

Kudos [?]: 160 [0], given: 134

Re: Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

08 Aug 2013, 11:17

VeritasPrepRon wrote:
WholeLottaLove wrote:
Two buses are travelling on the highway from X to Y . The speed of the first bus is 60KMPH and the second bus travels at the speed of 40KMPH. The first bus leaves at 11 AM and the second leaves 15 mins later. The first bus starts back for X, 15 mins after it reaches Y . How far from Y will the first Bus meet the second ?Also, after how much time will they meet each other after the departure of the first bus from X , if the distance between X and Y is 180 KM.

Round trip from X to Y to X. Distance is 180 km. Round trip = 360 km.

Bus A speed: 60 km/hour
leaves at 11:00 AM
Turns around 15 minutes after it reaches Y
Bus B speed: 40 km/hour
Leaves at 11:15 AM

Bus A reaches Y at 2:00 PM and heads back at 2:15 PM.
By the time bus A heads back, bus B has traveled for 3 hours meaning it has covered 120 km. At 2:15, bus A and bus B are 60 km apart. We can treat closing velocity as a combination of both speeds. In other words, time = distance/rate ===> time = 60/(40km/h + 60 km/h) ===> time = 60km/100km ===> time = .6 hours = 36 minutes. We know that it will take 36 minutes for B to meet A from the time when B has traveled 120 km which means that B will have traveled 3 hours + 36 minutes = 3:36 when they meet. B travels at 40 km/h so in 36 minutes it travels: distance=rate*time ===> distance = 40km/h*.6 ===> it travels an additional 24 km. B is a total of 180-120-24 = 36 km away from Y.

ANSWER: A)36 KM , 3 Hrs 36 Mins

Hey wholelottalove, I think you forgot to add back the 15 minutes that the bus waited at location Y. It drove for 3 hours one way and 36 minutes the other, but there was a respite of 15 minutes, hence why 3:51 and not 3:36.

On a side note, I've never seen an actual GMAT question with multiple components to solve like this one. It's a good question to solve, but it's not a real GMAT question.

Thanks!
-Ron
Senior Manager
Joined: 10 Jul 2013
Posts: 335
Followers: 3

Kudos [?]: 312 [1] , given: 102

Re: Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

08 Aug 2013, 11:41
1
KUDOS
guerrero25 wrote:
Two buses are travelling on the highway from X to Y . The speed of the first bus is 60KMPH and the second bus travels at the speed of 40KMPH. The first bus leaves at 11 AM and the second leaves 15 mins later. The first bus starts back for X, 15 mins after it reaches Y . How far from Y will the first Bus meet the second ?Also, after how much time will they meet each other after the departure of the first bus from X , if the distance between X and Y is 180 KM.

A)36 KM , 3 Hrs 36 Mins
B)36 KM, 3 Hrs 51 Mins
c)24KM, 3 Hrs 50 mins
d)24 KM, 3 hrs 51 mins
e)48 KM, 2 Hrs 51 mins

.............
solution:
Time to each Y, 1st bus = 180/60 = 3hours,
then 15 min rest. 2nd bus leaves 15 min later. so it also travels 3 hours.
distance covered by 2nd bus= 40 * 3 = 120
]so from y they are 180-120=60 km apart .

let, they will meet P km from Y after t hours.

now, P = 60 * t
and, 60-P = 40 * t
...............................
(+), 60 = 100t
or, t = 3/5
so p = 60 * 3/5 = 36km (Ans)
total time from the 1st = 3hour and15min+3/5 * 60 = 3hours and 51min (Answer)
_________________

Asif vai.....

Intern
Joined: 09 Jun 2015
Posts: 4
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: Two buses are travelling on the highway from X to Y . [#permalink]

Show Tags

11 Jun 2015, 02:18
Another way to quickly solve is to substitute the answers:

We know bus A goes 1 km per minute. We know bus A left Y at 3:15.

A) 36 km in 21 minutes, impossible
C) 24 km in 35 minutes, impossible
D) 24 km in 36 minutes, impossible
E) 48 km in -24 minutes impossible

B) 36 km in 36 minutes, only possible answer.
Re: Two buses are travelling on the highway from X to Y .   [#permalink] 11 Jun 2015, 02:18
Similar topics Replies Last post
Similar
Topics:
1 Two cars start at the same time from opposite ends of a highway that 6 02 Jun 2016, 03:35
21 Cars A and B are traveling from Town X to Town Y on the same route at 8 09 Jan 2015, 14:44
8 Buses A and B start from a common bus stop X. Bus A begins 5 20 Aug 2013, 17:22
6 Two highways start from a point P and meet again... 5 13 Feb 2013, 22:56
41 Two trains, X and Y, started simultaneously from opposite 8 30 Nov 2010, 05:30
Display posts from previous: Sort by