A runs 25% faster than B and is able to allow B a lead of 7 meters to

Question

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

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

Mathivanan Palraj · Accepted Answer

The ratio their speeds is 5:4; therefore the ratio of distance covered by them will also be 5:4
The difference in the ratio of distance is 1, that corresponds to the lead of 7 meters.
Therefore, length of race =5*7=35 meters

EgmatQuantExpert · Answer

Solution

Given:  
• A runs 25% faster than B
• A allow B a lead of 7 meters to end a race in dead heat

To find:  
• What is the length of the race?

Approach and Working out:  
• Let speed of B= S then A’s speed= 5/4 S
Now, if we assume race track to be of length x then A ran x metres in the same time as B took to cover x-7.
• x/ 5S /4= x-7/ S
• 4X/5S= x-7/S
• 5x- 35=4x
• x= 35
  Answer: D

gracie · Answer

let d=length of race
r=B's rate
because times of A and B are equal,
then d/(5r/4)=(d-7)/r
d=35 meters

Salsanousi · Answer

Another approach would be to let speed of B be 4 and speed of A = 4 * 1.25 = 5

Now B starts at 7 then move 4s

7,11,15,19,23,27,31,35

A starts at 0,5,10,15,20,25,30,35

Answer choice D.

Posted from my mobile device

mbafinhopeful · Answer

Let the length of the race be  d , B runs  (d-7)  meters and A runs  d  meters, in  s  mph and  1.25s  mph respectively.

time = \frac{distance}{speed}

Time taken by A =  \frac{d}{1.25s}

Time taken by B =  \frac{d-7}{s}

Since the race was a dead heat  \frac{d}{1.25s} = \frac{d-7}{s}

ds = 1.25ds - 8.75s

d = 1.25d - 8.75

d = \frac{8.75}{0.25} = 35 .

pushpitkc · Answer

If B's usual rate of running the race is 4x, A's rate will be 5x

Since the distances covered by both of them are equal provided A covers
7m less, we can equate the distances. So,  5x = 4x + 7  ->  x = 7

Therefore, the total length of the race is  5x  =  35 meters(Option D)

dave13 · Answer

\frac{x}{125} = \frac{x-7}{100}

(x-7)125 = 100x

125x-100x=875

25x=875

x = 35

ScottTargetTestPrep · Answer

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: D

PetoMargaryan · Answer

Alternative Approach.

Using the Gap formula, we Suppose that B is 7 meters ahead of A when starting the race. It means that 
Meeting time = Gap/(Va-Vb) = 7/(1.25-1) = 28 meters.

Now the problem says that A is ahead of B at the moment of ending the race by 7 meters. So the race distance is = 28 + 7 = 35

Posted from my mobile device

LeoN88 · Answer

A can cover d in t time. B can cover d-7 in t time.
So here time t is constant for A and B, let d be the distance for track-

d/125 = (d-7)/100

d= 35

tothepoint · Answer

I saw it this way.
The speed is 25% more, which is 1/4 more. Therefore the distance covered will be 1/5th less in the same time. 1/5th is given to us as 7. So the actual distance will be 35.

Posted from my mobile device

Adit_ · Answer

Ratio of speeds = 5:4
There is a difference of 1 metre for each time interval they run and at same time A bridges 7 metres gap.
It means that 5*7:4*7 = 35:28 is the distances travelled giving us 7 metre gap.
Thus total length =  35 .

A runs 25% faster than B and is able to allow B a lead of 7 meters to

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A runs 25% faster than B and is able to allow B a lead of 7 meters to

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards