one starting at each end

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Oct 17, 2011 2:01 am

Using his bike, Daryl can complete a paper route in 20 minutes. Francisco, who walks the route, can complete it in 30 minutes. How long will it take the two boys to complete the route if they work together, one starting at each end of the route?
(A) 8 minutes
(B) 12 minutes
(C) 20 minutes
(D) 30 minutes
(E) 45 minutes

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Source: Beat The GMAT — Problem Solving | Mon Oct 17, 2011 2:01 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Oct 17, 2011 2:05 am

x/20 + x/30 = 1.

x = 12 B

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Oct 17, 2011 2:13 am

Let the total length of the paper track be d

Daryl's Speed = d/20 distance units/minute
Francisco's Speed = d/30 distance units/minute

As they are travelling towards each other relative speed would be the sum of speeds i.e.

Relative speed:(d/30) + (d/20)
Distance travelled = d
time taken = distance/relative speed = d/ ((d/30) + (d/20)) = 12 Option B

Last edited by neelgandham on Mon Oct 17, 2011 2:14 am, edited 1 time in total.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Oct 17, 2011 2:14 am

sanju09 wrote:Using his bike, Daryl can complete a paper route in 20 minutes. Francisco, who walks the route, can complete it in 30 minutes. How long will it take the two boys to complete the route if they work together, one starting at each end of the route?
(A) 8 minutes
(B) 12 minutes
(C) 20 minutes
(D) 30 minutes
(E) 45 minutes

In 1 minute, Daryl travels 1/20 of distance.
In 1 minute, Francisco travels 1/30 of distance.
Then in 1 minute, Daryl + Francisco travels 1/20 + 1/30 = 50/600 = 1/12 of distance
So, both of them together take 12 minutes to complete the route.

The correct answer is B.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Oct 17, 2011 3:06 am

sanju09 wrote:Using his bike, Daryl can complete a paper route in 20 minutes. Francisco, who walks the route, can complete it in 30 minutes. How long will it take the two boys to complete the route if they work together, one starting at each end of the route?
(A) 8 minutes
(B) 12 minutes
(C) 20 minutes
(D) 30 minutes
(E) 45 minutes

Let the route = 60 meters.
Rate for Daryl = d/t = 60/20 = 3 meters per minute.
Rate for Francisco = d/t = 60/30 = 2 meters per minute.
Combined rate for Daryl and Francisco = 3+2 = 5 meters per minute.
Time for Daryl and Francisco to meet = d/r = 60/5 = 12 minutes.

The correct answer is B.

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon Oct 17, 2011 3:39 am

IMO: B; way too easy, wish to get these kind of questions in real CAT

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