Speed, race

Notice that the distance that A runs 7 meters more than B, so:

d_a = d_b + 7

Since distance = rate * time, re-write this:

(r_a)(t_a) = (r_b)(t_b) + 7

Since A runs 25% faster than B, re-write as follows:

(1.25*r_b)(t_a) = (r_b)(t_b) + 7

Now, the other catch is that they finish in dead heat, so their times are equal, so change t_a to t_b

(1.25*r_b)(t_b) - (r_b)(t_b) = 7

(1.25*r_b)(t_b) - (r_b)(t_b) = 7

(1.25 - 1)(r_b*t_b) = 7

r_b*t_b = 7 / .25

d_b = 28

Since B goes 28 meters, that means A goes 35 meters, so the length of the race is 35 meters.

francoisph 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?

let the race be of x metre
speed of b=y
speed of a=1.25y
distance travelled by a=x
distance travelled by b=x-7 m
now since this is dead heat they both reach end at same time
time taken by a=x/1.25y
time taken by B=x-7/y
x/1.25y=(x-7)/y
x=1.25x-8.75
8.75=0.25 x
x=35 metre
so distance =35 metre

We know A's rate is 1.25B. Let B's rate be 1. Then, A's rate is 1.25

Since we have 2 objects travelling in the same direction, we should subtract the rates:

1.25 - 1 = 0.25

This is the rate at which A is catching up to B. We know that in order to catch up, A must close the distance between itself and B. Thus, using speed = distance/time, we have:

0.25 = 7/t

t = 28 (units of time)

So, they both travelled for 28 time-units (minutes, seconds, who cares). Since B's rate is 1, B has travelled 28 meters. Because B had a 7-meter headstart on A, A has travelled 28 + 7 = 35 meters, the length of the track. (Or, A's rate is 1.25; thus, A travelled 1.25*28 = 35 meters, the length of the track).

And here's a good take-away for 2 moving-object problems:

https://www.beatthegmat.com/speed-train- ... tml#265142

I did it in a little bit subjective manner....

For every 7 meter of B's run A is coming close by .25 therefore for the dead beat it will require 7/.25=28 meter to run.

Please let me know if my strategy is wrong.

thanks.

Asif wrote:I did it in a little bit subjective manner....

For every 7 meter of B's run A is coming close by .25 therefore for the dead beat it will require 7/.25=28 meter to run.

Please let me know if my strategy is wrong.

thanks.

your reasoning is sound!

Hi All !

I am new to this forum. Just warming up for the GMAT prep (its not an excuse. The realization that I need to start dawned today ! ).

I love the different approaches given here. However, I have an issue with the question ! The question does not mention whether the head start given by A is within the distance of the race or outside it, that is - whether B starts from the start line and A starts the race from 7 meters behind the actual start line or whether A starts the race from the start line, B starts 7 meters ahead of the start line.

The length of the race in this case will depend on who covers the full distance and this information is missing.

Am I thinking too much ???

OA is distance =35 metre

no meaning discussing question without options. in gmat we have less than 2 minutes for a question so kindly give options to save other peoples time

The question does not mention whether the head start given by A is within the distance of the race or outside it,

I thought the same thing at first!

But then I interepreted "headstart" as B is 7 meters ahead of the start line while A begins at the start line.