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# A man cycling along the road noticed that every 12 minutes

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: A man cycling along the road noticed that every 12 minutes [#permalink]

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24 Apr 2017, 01:07
1
manishtank1988 wrote:
Hello Experts,
msk0657, Vyshak, abhimahna, Engr2012, Abhishek009, Skywalker18, VeritasPrepKarishma, Bunuel, mikemcgarry, ehsan090, gracie, ScottTargetTestPrep, rohit8865, alpham, tiklimumita, Nunuboy1994, maheshaero20

Can you someone please clarify what i am thinking/understanding from the question is correct or not:
I am not able to understand that how come within 12 or 4 minutes entire distance d is being traversed?
So after going over all the explanation on this thread and veritas page (url: http://www.veritasprep.com/blog/2012/08 ... -concepts/) i think i understand the given question as follows:

And based on this we get d = 12(b - c) = 4(b + c)
=> 12b - 12c = 4b + 4c
=> 8b = 16c
=> b = 2c

d = 12b−6b = 6b
Interval x = (between 2 buses leaving the same location/station)
Interval x = d/b = 6 | B

NOTE: speed of bus = b = s2 & speed of cyclist = c = s1

And based on this we get d = 12(b - c) = 4(b + c)

From where did you get 4(b + c)?

The oncoming bus takes 6 mins to meet so it should be

d = 12(b - c) = 6(b + c)
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Re: A man cycling along the road noticed that every 12 minutes [#permalink]

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10 Jun 2017, 09:52
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?

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: $$\frac{d}{b+c}=4$$, $$d=4b+4c$$;

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

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

Hope it helps.

Bunuel Why is the distance when the bus overtakes the bicycle in 12 minutes and the distance when the bicycle is met by the opposing bus in 4 minutes same??? Please clarify. Thanks.

Posted from my mobile device
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Posts: 46207
Re: A man cycling along the road noticed that every 12 minutes [#permalink]

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10 Jun 2017, 10:16
Romannepal 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?

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: $$\frac{d}{b+c}=4$$, $$d=4b+4c$$;

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

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

Hope it helps.

Bunuel Why is the distance when the bus overtakes the bicycle in 12 minutes and the distance when the bicycle is met by the opposing bus in 4 minutes same??? Please clarify. Thanks.

Posted from my mobile device

In once case a man is moving towards the bus and thus the relative speed is higher, which gives smaller time intervals and in another case a man is moving away from the bus and thus the relative speed is lower, which gives greater time intervals.
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Re: A man cycling along the road noticed that every 12 minutes [#permalink]

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03 Jul 2017, 05:50
If we assume the cyclist is standing still 1 mile between both buses. Then, either add the speeds and multiply by the total distance.

i.e 1/4+1/12 = 1/3; combined time is 3 and now multiply by 2 to get the time interval of 6.

or

Again assuming the cyclist is still and between both buses, just subtract the speeds of the buses to get the absolute difference (interval) between their arrivals.

Conceptually, this question is similar to number line questions and could also be a great data sufficiency question.

i.e 1/4- 1/12 =1/6 and time interval =6.
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Re: A man cycling along the road noticed that every 12 minutes [#permalink]

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29 Jan 2018, 11:08
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

We can let b = speed of the bus and c = speed of the cyclist. Let d = the distance between two consecutive buses (in the same direction). Thus, we want to determine d/b, which is the time interval between two consecutive buses.

When the bus and the cyclist are traveling in the same direction, if we assume a bus overtakes the cyclist at a certain time, then it will be 12 minutes until the next bus overtakes him. Thus, we have:

12(b - c) = d

12b - 12c = d

When the bus and the cyclist are traveling in opposite directions, if we assume the cyclist meets an oncoming bus at a certain time, then it will be 4 minutes until the cyclist meets the next oncoming bus. Thus, we have:

4(b + c) = d

4b + 4c = d

Subtracting 4b + 4c = d from 12b - 12c = d, we have:

8b - 16c = 0

8b = 16c

b = 2c

We see that the bus is twice as fast as the cyclist. Substituting 2c for b in 12(b - c) = d (or in 4(b + c) = d), we have:

12(2c - c) = d

12c = d

Recall that the time interval between two consecutive buses is d/b; thus, we have:

d/b = 12c/2c = 6

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Re: A man cycling along the road noticed that every 12 minutes   [#permalink] 29 Jan 2018, 11:08

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