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

one starting at each end

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 am; Thanked: 230 times; Followed by:21 members

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 am; Location: Utrecht, The Netherlands; Thanked: 318 times; Followed by:52 members

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 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; 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 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; 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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