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# A man sets out to cycle from BBSR to CTC and at the same

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Manager
Joined: 27 Jul 2011
Posts: 129
A man sets out to cycle from BBSR to CTC and at the same  [#permalink]

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30 Jun 2012, 23:45
1
19
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:37) correct 57% (02:14) wrong based on 215 sessions

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A man sets out to cycle from BBSR to CTC and at the same time another man starts from CTC to BBSR. After passing each other they complete their journeys in 4 and 9 hrs respectively. At what rate does the second man cycle if the first one cycles at 9 km/hr.

A. 4 km/hr
B. 6 km/hr
C. 8 km/hr
D. 9 km/hr
E. can't be determined

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Re: A man sets out to cycle from BBSR to CTC and at the same  [#permalink]

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22 Oct 2014, 20:32
7
3
BukrsGmat wrote:
A man sets out to cycle from BBSR to CTC and at the same time another man starts from CTC to BBSR. After passing each other they complete their journeys in 4 and 9 hrs respectively. At what rate does the second man cycle if the first one cycles at 9 km/hr.

A. 4 km/hr
B. 6 km/hr
C. 8 km/hr
D. 9 km/hr
E. can't be determined

You can use the formula or the ratio approach.

Formula:

If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:

$$Sa/Sb = \sqrt{(b/a)} = \sqrt{9/4} = 3/2$$

So the ratio of speeds of first man and second man is 3:2
If the first man cycles at 9 km/hr (which is 3*3), the second will cycle at 2*3 = 6 km/hr

Check out another approach in this post (the question in the post uses almost same values):
http://www.veritasprep.com/blog/2013/04 ... -formulas/
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Re: A man sets out to cycle from BBSR to CTC  [#permalink]

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01 Jul 2012, 02:01
2
2
sujit2k7 wrote:
A man sets out to cycle from BBSR to CTC and at the same time another man starts from CTC to BBSR. After passing each other they complete their journeys in 4 and 9 hrs respectively . At what rate does the second man cycle if the first one cycles at 9 km/hr.

a) 4km/hr
b) 6km/hr
c) 8 km/hr
d) 9 km/hr
e) can't be determined

Hi,

let the speed of second person by x,
and the time taken by them to meet is t,
also, we know that speed of first person is 9km/hr

(BBSR)A------------------------C---------------B(CTC)
supposing they meet at C,
so, distance traveled by first person in t time = distance traveled by second person in 9hrs (=AC)
or 9t=x*9
or x = t
similarly, distance traveled by second person in t time = distance traveled by second person in 4hrs (=CB)
or x*t = 9*4
or $$x^2=36$$
or x=6km/hr

Regards,
Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: A man sets out to cycle from BBSR to CTC and at the same  [#permalink]

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01 Jul 2012, 03:01
sujit2k7 wrote:
A man sets out to cycle from BBSR to CTC and at the same time another man starts from CTC to BBSR. After passing each other they complete their journeys in 4 and 9 hrs respectively. At what rate does the second man cycle if the first one cycles at 9 km/hr.

A. 4 km/hr
B. 6 km/hr
C. 8 km/hr
D. 9 km/hr
E. can't be determined

Check similar question to practice: two-cars-a-and-b-start-from-boston-and-new-york-respectively-131507.html

Hope it helps.
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Manager
Joined: 14 Oct 2012
Posts: 160
Re: A man sets out to cycle from BBSR to CTC and at the same  [#permalink]

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23 Apr 2017, 21:06
1
My 2 cents:
I hope this theoretical construct helps everyone understand the various relationships for this type of sums:

Attachments

sa_sb.jpg [ 1012.76 KiB | Viewed 4103 times ]

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Joined: 09 Sep 2013
Posts: 13247
Re: A man sets out to cycle from BBSR to CTC and at the same  [#permalink]

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16 Jul 2019, 10:26
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Re: A man sets out to cycle from BBSR to CTC and at the same   [#permalink] 16 Jul 2019, 10:26
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