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A man cycling along the road noticed that every 12 minutes

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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 15 Jul 2012, 20:09
why is the distance between buses a constant value?
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 15 Jul 2012, 21:38
Expert's post
teal wrote:
why is the distance between buses a constant value?


Assume that starting from a bus station, all buses run at the same speed of 50 mph.
Say a bus starts at 12:00 noon. Another starts at 1:00 pm i.e. exactly one hr later on the same route. Can we say that the previous bus is 50 miles away at 1:00 pm? Yes, so the distance between the two buses initially will be 50 miles. The 1 o clock bus also runs at 50 mph. Will the distance between these two buses always stay the same i.e. the initial 50 miles? Since both buses are moving at the same speed of 50 mph, relative to each other, they are not moving at all and the distance between them remains constant.

The exact same concept is used in this question.
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Re: test m08 question n18 [#permalink] New post 15 Jul 2012, 22:49
Bunuel wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!


A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.

Let the speed of cyclist be c.

Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;

Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;

d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.

Interval=\frac{d}{b}=\frac{6b}{b}=6

Answer: B (6 minutes).

Hope it helps.



Hi,

I m not sure how this formula of Interval has been arrived?. Is it a standard formula???

Thanks in advance... :-D
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 16 Jul 2012, 04:02
Expert's post
teal wrote:
why is the distance between buses a constant value?


Buses travel on schedule so, the distance between two successive buses must be some constant value.

bhavinshah5685 wrote:
Hi,

I m not sure how this formula of Interval has been arrived?. Is it a standard formula???

Thanks in advance... :-D


Interval between two successive buses is the time, so it equals time=distance/rate.
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 16 Jul 2012, 08:20
VeritasPrepKarishma & Bunuel, great replies! Methods are different, similar concepts! Thanks for posting guys +1 to you
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 24 Aug 2012, 22:52
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lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!


When solving motion problems, I can't do without some drawings.
So, here is my version:

Denote by B the speed of the bus and by C the speed of the bicycle. Both are assumed to be constant.
Let T be the constant time interval between consecutive buses. It means, the distance between two consecutive buses is BT.

First scenario: buses and bicycle moving in the same direction and buses overtake the bicycle. Refer to the first attached drawing.

When bus B and bicycle C are at point n, next bus B^* is at point m.
Bus B^* will overtake bicycle C at point p.
In 12 minutes, bus B^* travels the distance mp and bicycle C travels the distance np.
We know that mp is the distance between consecutive buses, therefore mp=BT.
Translated into an equation mp=mn+np, so:
12B=BT+12C (1)

Second scenario: buses and bicycle moving in opposite directions and buses meet the bicycle. Refer to the second attached drawing.

When bus B and bicycle C are at point m, next bus B^* is at point p.
Bus B^* will meet bicycle C at point n.
In 4 minutes, bus B^* travels the distance np and bicycle C travels the distance mn.
We know that mp is the distance between consecutive buses, therefore mp=BT.
Translated into an equation mp=mn+np, so:
BT=4C+4B (2)

Expressing BT from both equations, we get 12(B-C)=4(B+C) from which B=2C (3)
Substituting (3) in (2) for example, we get, 2CT=8C+4C from which T=6 (minutes).

Answer B.
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Re: test m08 question n18 [#permalink] New post 21 Jun 2013, 13:49
Bunuel wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!


A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.

Let the speed of cyclist be c.

Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;

Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;

d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.

Interval=\frac{d}{b}=\frac{6b}{b}=6

Answer: B (6 minutes).

Hope it helps.




what does " every 4 minutes he meets an oncoming bus. " refers? please help
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Re: test m08 question n18 [#permalink] New post 21 Jun 2013, 14:12
FTGNGU wrote:
Bunuel wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!


A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.

Let the speed of cyclist be c.

Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;

Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;

d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.

Interval=\frac{d}{b}=\frac{6b}{b}=6

Answer: B (6 minutes).

Hope it helps.




what does " every 4 minutes he meets an oncoming bus. " refers? please help


FTGNGU,
it means every 4 minutes, the cyclist meets a bus moving in opposite direction. So, the relative speed between them is the absolute value of [speed of cyclist - speed of the bus]

Hope it helps,
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Re: test m08 question n18 [#permalink] New post 23 Jun 2013, 20:26
Expert's post
FTGNGU wrote:

what does " every 4 minutes he meets an oncoming bus. " refers? please help


The cyclist is moving in one direction, say due east. Every 4 mins, he meets a bus coming towards him (going due West)


Cyc ----> <-------- Bus (Bus coming towards him)

Cyc-><-Bus (Meets the bus)

<------Bus Cycl -------> (They cross each other)

This happens with a different bus every 4 mins.


Every 4 mins, he meets an oncoming bus. So he meets a bus coming towards him at 12:00 noon. Then, at 12:04 pm, he meets another bus coming towards him. Then again at 12:08 pm and so on.

Their relative speed = Speed of cyclist + Speed of Bus
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 23 Jun 2013, 22:41
1. In the case of the overtaking bus, the speed of the cyclist needs to be deducted from that of the bus and in the case of the oncoming bus their
speed needs to be added.
2. These two speeds are in the ratio 1:3 because the time is in the ratio 3:1.
3. s1+s2 =3x -----(1) and s2-s1 = x --- (2) Therefore s2 = 2x --- (3) where s1 is the speed of the cyclist and s2 is the speed of the bus.
4. To find the time interval between consecutive buses, we need to assume the case when the buses alone are running and the cyclist is stationary. That is we need to consider s2 only and assume s1=0.
5. From (1) and (3) we know that the speed of (3) is 1.5 times less than the speed of (1.) Therefore the time taken will be 1.5 times more than in the case of (1)
6. In the case of (1), the time taken is 4 min. Therefore in the case of (3) it is 4*1.5=6 min. That is when the cyclist is stationary, the buses cross him every 6 min.

Therefore the time interval between 2 consecutive buses is 6 min
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Last edited by SravnaTestPrep on 16 Aug 2013, 18:41, edited 2 times in total.
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 23 Jun 2013, 23:24
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Another approach:

1. Assume the combined speed of the cyclist and the bus is s1+ s2. s1 is the speed of the cyclist and s2 is the speed of the bus.
2. From the time a bus starts till the time it meets the cyclist, assume the distance traveled is d and the time taken is m
3. In the case of overtaking the difference in the speeds needs to be taken since both are traveling in the same direction. The relative speed is s2- s1. Assume to travel the same distance d the time taken is n
5. From (2) and (3), we have, m(s1+s2) = n(s2-s1)=d. we know m is 4 min and n is 12 min.
6. d= 4(s1+s2) = 12(s2-s1)
7. We want to find d/ s2 = 12(s2-s1)/s2 = 12(s2/s2) - 12(s1/s2) = 12-6= 6 min
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 08 Aug 2013, 16:13
Hello.

While I understand the algebra behind the problem, I'm not sure I understand the logic. Consecutive buses are passed every four minutes and the cyclist is passed every 12. I'm unable to rationalize how the time between consecutive buses is 6 minutes? I'm not even sure I understand the context of "consecutive" in this problem.

Thanks!!! :-D
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 09 Aug 2013, 01:22
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!



Time interval between consecutive buses!!!!!
Already given !!!!

this question is FLAWED.......
We can calculate when they will overtake each other.....
100% FLAWED question
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 09 Aug 2013, 01:25
Expert's post
Asifpirlo wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!



Time interval between consecutive buses!!!!!
Already given !!!!

this question is FLAWED.......
We can calculate when they will overtake each other.....
100% FLAWED question


Hello, It will be interesting to understand your logic behind branding this question as '100 % flawed"? Can you kindly elucidate?
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 09 Aug 2013, 08:04
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While I wouldn't say the question is flawed, the wording is quite ambiguous.

mau5 wrote:
Asifpirlo wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!



Time interval between consecutive buses!!!!!
Already given !!!!

this question is FLAWED.......
We can calculate when they will overtake each other.....
100% FLAWED question


Hello, It will be interesting to understand your logic behind branding this question as '100 % flawed"? Can you kindly elucidate?
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 09 Aug 2013, 12:35
mau5 wrote:
Asifpirlo wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!



Time interval between consecutive buses!!!!!
Already given !!!!

this question is FLAWED.......
We can calculate when they will overtake each other.....
100% FLAWED question


Hello, It will be interesting to understand your logic behind branding this question as '100 % flawed"? Can you kindly elucidate?



i already mentioned but may be you didn't see.
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 13 Aug 2013, 12:03
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

This problem took me a while to figure out but I think I got it!

The interval refers to the time (i.e. time = distance/speed)

The interval for the bus is t=d/b where b represents the constant speed of both buses.

When the bus overtakes the cyclist, it represents the bus gaining on the cyclist (i.e. the bus speed is faster than the cyclist) so every time the bus overtakes the cyclist, which is every 12 minutes, we have:

12 = d/(b-c) where b-c is the rate that the bus gains on the cyclist.
12b-12c = d

When the oncoming bus meets the cyclist, it represents their combined forward speeds towards one another. Every time the bus meets the cyclist, which is every 4 minutes, we have:

4 = d/(b+c)
4b+4c = d
Note, we use c for both bus speeds because the question tells us that they move at the same constant speed.

12b-12c = d
4b+4c = d

12b-12c = 4b+4c
8b = 16c
b = 2c

12b-12c = d
12(2c) - 12c = d

My problem is this: how do I know to solve for d? In other words, why would I know:
b = 2c, 12b-12c = d
12*(2c) - 12c = d
24c - 12c = d
12c = d isn't correct?
How would I know to convert b=2c to c=b/2 to plug in so I can get a value for d thus getting me the right answer?


c=b/2
12b-12c = d
12b - 12(b/2) = d
12b - 6b = d
6b = d

t=d/b (the interval for both buses)
t=(6b/b)
t = 6

ANSWER: B. 6 minutes
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Re: test m08 question n18 [#permalink] New post 16 Aug 2013, 01:20
Bunuel wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!


A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.

Let the speed of cyclist be c.

Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;

Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;

d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.

Interval=\frac{d}{b}=\frac{6b}{b}=6

Answer: B (6 minutes).

Hope it helps.


Hi Bunuel
Following doubts need to be clear

d/b-c---Why it is so if objects are moving in same direction.
d/b+c---Why it is so if objects are moving in opposite direction.

Rgds
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Re: test m08 question n18 [#permalink] New post 16 Aug 2013, 01:23
Expert's post
prasannajeet wrote:
Bunuel wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!


A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.

Let the speed of cyclist be c.

Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;

Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;

d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.

Interval=\frac{d}{b}=\frac{6b}{b}=6

Answer: B (6 minutes).

Hope it helps.


Hi Bunuel
Following doubts need to be clear

d/b-c---Why it is so if objects are moving in same direction.
d/b+c---Why it is so if objects are moving in opposite direction.

Rgds
Prasannajeet


When 2 objects move in the same direction their relative speed is the difference of their individual speeds.
When 2 objects move in the opposite direction their relative speed is the sum of their individual speeds.
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Re: A man cycling along the road noticed that every 12 minutes [#permalink] New post 16 Aug 2013, 01:24
Expert's post
Asifpirlo wrote:
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

A. 5 minutes
B. 6 minutes
C. 8 minutes
D. 9 minutes
E. 10 minutes

I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test?
Thank you in advance!!



Time interval between consecutive buses!!!!!
Already given !!!!

this question is FLAWED.......
We can calculate when they will overtake each other.....
100% FLAWED question


There is nothing wrong with the question.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A man cycling along the road noticed that every 12 minutes   [#permalink] 16 Aug 2013, 01:24
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