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Race- Dead Heat

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by kanha81 » Thu Apr 09, 2009 2:55 pm
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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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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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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