cyclist

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ritula: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Sun Aug 10, 2008 8:35 pm

by ritula » Tue Sep 23, 2008 2:57 am

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

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes

Philosophers have interpreted world in various ways, the point is to change it!

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Source: Beat The GMAT — Problem Solving | Tue Sep 23, 2008 2:57 am

Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

by Morgoth » Tue Sep 23, 2008 4:24 am

I think this question is not only badly worded but also unclear on what exactly needs to be calculated. I could be wrong, does anybody else thinks the same.

Source pls?

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Tue Sep 23, 2008 6:50 am

between what consecutive buses?

oncoming? passing?

Agree with Morgoth

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ritula: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Sun Aug 10, 2008 8:35 pm

Cant help it

by ritula » Tue Sep 23, 2008 7:07 am

cant help it. I havent framed the question myself. couldnt understand. dats y posted here.

Morgoth wrote:I think this question is not only badly worded but also unclear on what exactly needs to be calculated. I could be wrong, does anybody else thinks the same.

Source pls?

Philosophers have interpreted world in various ways, the point is to change it!

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niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 amFollowed by: 1 member; Location: USA; Thanked: 13 times

by niraj_a » Tue Sep 23, 2008 8:14 am

source?

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

Re: cyclist

by sudhir3127 » Tue Sep 23, 2008 8:22 am

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

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes

i think its B 6.

relative speed formula

2XY/(X+Y)

2*12*4/16
= 6

Hope that helps..

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stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

by stop@800 » Tue Sep 23, 2008 1:11 pm

A very good question:

Let x be speed of cycle and [in km / minutes]
Let y be speed of bus.

In straight direction:
man is moving at x speed and bus is following him at y speed.
Relative speed = (y-x) [y has to be greater than x for bus to catch the cycle]
and after 12 minutes they catch each other so distance traveled is 12*(y-x)

In opposite direction:
man is moving at x speed and bus is coming towards him at y speed.
Relative speed = (y+x)
and after 4 minutes they catch each other so distance traveled is 4*(x+y)

Since time interval between buses is constant and the speed of bus is also constant so
these two distances must be equal.
4*(x+y) = 12*(y-x)

Solve it you will get y = 2*x

Now the time interval between two buses will be = distance traveled / speed of bus
time = (4x+4y)/y or = (12*(y-x)/y)

substitute y = 2x and solve it you will get your answer.

www.interrogationpoint.com

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ritula: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Sun Aug 10, 2008 8:35 pm

Re:

by ritula » Tue Sep 23, 2008 8:40 pm

U r a genius

stop@800 wrote:A very good question:

Let x be speed of cycle and [in km / minutes]
Let y be speed of bus.

In straight direction:
man is moving at x speed and bus is following him at y speed.
Relative speed = (y-x) [y has to be greater than x for bus to catch the cycle]
and after 12 minutes they catch each other so distance traveled is 12*(y-x)

In opposite direction:
man is moving at x speed and bus is coming towards him at y speed.
Relative speed = (y+x)
and after 4 minutes they catch each other so distance traveled is 4*(x+y)

Since time interval between buses is constant and the speed of bus is also constant so
these two distances must be equal.
4*(x+y) = 12*(y-x)

Solve it you will get y = 2*x

Now the time interval between two buses will be = distance traveled / speed of bus
time = (4x+4y)/y or = (12*(y-x)/y)

substitute y = 2x and solve it you will get your answer.

Philosophers have interpreted world in various ways, the point is to change it!

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tparekh: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Jun 20, 2008 12:04 pm

Re: cyclist

by tparekh » Wed Sep 24, 2008 12:01 am

sudhir3127 wrote:
ritula wrote:A man cycling along the road noticed that every 12 minutes a bus overtakes him while every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes
i think its B 6.

relative speed formula

2XY/(X+Y)

2*12*4/16
= 6

Hope that helps..

Can you explain the relative speed formula?

Like this post

stop@800: Legendary Member; Posts: 871; Joined: Wed Aug 13, 2008 7:48 am; Thanked: 48 times

Re: cyclist

by stop@800 » Wed Sep 24, 2008 6:27 am

This is actually average speed formula: [when distance is same]

Let say A person moves from point A to point B with x speed and comes back with y speed than average speed will be given by (2xy)/(x+y)

Ex:
A cyclist covered 50 m forward direction in 5 m/s and came back with speed 3 m/s what is his avg speed?

avg = 2*5*3/(5+3) = 30/8 = 3.75

Yes!! It will not be 4. Be careful

The above question if you will solve with formula
avg speed = (total dis)/(total time)
You will get the same answer.

PS: The distance 50m is not needed, I have mentioned just for your better understanding.

tparekh wrote:
sudhir3127 wrote:
ritula wrote:A man cycling along the road noticed that every 12 minutes a bus overtakes him while every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes
i think its B 6.

relative speed formula

2XY/(X+Y)

2*12*4/16
= 6

Hope that helps..
Can you explain the relative speed formula?

www.interrogationpoint.com

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niraj_a: Legendary Member; Posts: 708; Joined: Sun Jun 01, 2008 4:59 amFollowed by: 1 member; Location: USA; Thanked: 13 times

by niraj_a » Wed Sep 24, 2008 7:49 am

sudhir

like stop@800 said, that definitely is the avg. speed formula, wouldn't apply in this case.

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