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# Ok so one idle afternoon praet , stoolfi , dj and Titleist

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Manager
Joined: 26 Aug 2003
Posts: 233
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Ok so one idle afternoon praet , stoolfi , dj and Titleist [#permalink]  07 Jan 2004, 08:06
Ok so one idle afternoon praet, stoolfi, dj and Titleist decide to hold a bicycle race on a track 1 mile in circumferance. To make the game interesting they decided that all four would ride BUT there will be only one round race. So basically one member of the team tags another. They divided up into following two teams by tossing a fair coin each:
Team 1 (tails): praet and stoolfi
Team 2 (heads): dj and Titleist

Rules:
* Every member must ride
* One member rides half way the track and then tags the 2nd. 2nd member finishes the lap.

To make it more interesting
* All four members' average speeds should average out to 60 miles/hr
* The two fastest members (could be from different teams) get the price unless all four tie.

Now half way the race (meaning after first team's turn) we know average speeds:
praet: 30 miles/hr
stoolfi: 30 miles/hr

How fast will dj and Titleist have to run to draw or to win the prize? Who will be the winner(s)? Show the logical steps and work, guys...

Last edited by wonder_gmat on 07 Jan 2004, 10:44, edited 4 times in total.
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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need to understand it better. you said:

Now half way the race we know average speeds:
praet: 30 miles/hr
stoolfi: 30 miles/hr

preat will run 1/2 and then stoolfi will run the rest. how do we know stoolfi's speed when it is only half done?... if we know, dj and titleist will try to run the same speed to draw the match..

what am I missing?
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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Kudos [?]: 35 [0], given: 0

half distance = 1/2 miles
time:
preat = stoolfi = 1/60 hrs
total time = 1/30 hrs = .033 hrs

average speed should be 60 miles/hr

possible speed:
dj & titleist
10:50
20:40
30:30
or vice versa

team 2 lost

okay, lets try some more..
1:59 ---- lost
25:35 ---- lost

the eq should be
X-speed of dj, 60-X speed of titleist
D distance travelled

D/X + D/(60-X) < 1/30
1/2X + 1/2(60-X) < 1/30

are we ever gonna win...I will tie

I won't run around the circle, I will rather take the diameterical route

I am still researching, anyway..

Last edited by dj on 07 Jan 2004, 10:42, edited 1 time in total.
Manager
Joined: 26 Aug 2003
Posts: 233
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dj:
I have changed the wording of the problem, after your first post, to make clearer.

Oh and I was going to add this to the rules: HAVE to run the circle to get back to your starting point, hence finish the lap!
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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Kudos [?]: 35 [0], given: 0

the best is to run at 30 miles/hr and tie the match
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