Two buses are travelling on the highway from X to Y . : GMAT Problem Solving (PS)
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# Two buses are travelling on the highway from X to Y .

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

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24 Jun 2013, 13:15
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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
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Re: Two buses are travelling on the highway from X to Y . [#permalink]

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

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25 Jun 2013, 00:31
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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.
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Last edited by Narenn on 26 Jun 2013, 08:38, edited 1 time in total.
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Re: Two buses are travelling on the highway from X to Y . [#permalink]

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

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08 Aug 2013, 10:51
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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
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Re: Two buses are travelling on the highway from X to Y . [#permalink]

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

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08 Aug 2013, 11:41
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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)
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Re: Two buses are travelling on the highway from X to Y . [#permalink]

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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
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