Race- Dead Heat

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kanha81: Master | Next Rank: 500 Posts; Posts: 431; Joined: Sat Jan 10, 2009 9:32 am; Thanked: 16 times; Followed by:1 members

Race- Dead Heat

by kanha81 » Thu Apr 09, 2009 2:55 pm

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A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?

A.10 meters
B. 25 meters
C. 45 meters
D. 15 meters
E. 35 meters

Can anyone please help solve the above problem?

Thanks!

OA [spoiler][E][/spoiler]

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Source: Beat The GMAT — Problem Solving | Thu Apr 09, 2009 2:55 pm

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Thu Apr 09, 2009 3:16 pm

Let's assume that the length of the race track is x meters and that Runner A's speed 1.25y and runner B's speed is y. Since the problem tells us that Runner A will finish the race with runner B in dead heat if he/she gives runner B a head start of 7 meters, we can already take into consideration that Runner A will finish at the same time as runner B when they finish the race. So:

x-7 is the distance that runner B will run since he/she gets a head start of 7 meters.

x is the distance that runner A will run.

x-7/y=x/1.25y
x-7/y=4x/5y
Multiply both sides by y and you get x-7=4x/5
x=35 E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Oct 03, 2018 4:36 pm

kanha81 wrote:A runs 25% faster than B and is able to give him a start of 7 meters to end a race in dead heat. What is the length of the race?

A.10 meters
B. 25 meters
C. 45 meters
D. 15 meters
E. 35 meters

Let the length of the race be represented by d and let the rate of runner B be represented by r. Since A runs 25% faster than B, the rate of A is 1.25r.

Since the times are the same, we can create the equation:

time for runner A = time for runner B

d/1.25r = (d - 7)/r

rd = 1.25r(d - 7)

d = 1.25d - 8.75

8.75 = 0.25d

35 = d

Answer: E

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