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

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Manager
Joined: 03 May 2017
Posts: 114
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.
Intern
Joined: 03 Dec 2016
Posts: 1
Re: A man cycling along the road noticed that every 12 minutes [#permalink]

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09 Oct 2017, 17:01
I'm a bit confused by the last part "d=12b−6b=6b." How did you get 12b and 6b?
Manager
Joined: 03 May 2017
Posts: 114
A man cycling along the road noticed that every 12 minutes [#permalink]

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09 Oct 2017, 20:24
jlstiles455 wrote:
I'm a bit confused by the last part "d=12b−6b=6b." How did you get 12b and 6b?

Hi,

If you are referring to Bunuel's explanation above. Note that from 4(b+c) =12(b-c) = d, we get 8b= 16c= d, and b=2c or c=b/2= 0.5b
Then If you substitute c for b, you had get d= 12(b-0.5b) = 4(b+0.5b) = 6b.

Best,
Target Test Prep Representative
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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]

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08 Feb 2018, 09:00
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.

Hi Bunuel. Why did you substract the cyclist speed from the bus speed for the overtaking part and added them for the meeting part?
Re: A man cycling along the road noticed that every 12 minutes   [#permalink] 08 Feb 2018, 09:00

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