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

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Math Expert
Joined: 02 Sep 2009
Posts: 51121
A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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14 Mar 2016, 06:23
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25% (medium)

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78% (01:38) correct 22% (02:54) wrong based on 209 sessions

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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

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Joined: 09 Jun 2015
Posts: 93
Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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14 Mar 2016, 20:48
1
5
Bunuel wrote:
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

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
##### General Discussion
VP
Joined: 07 Dec 2014
Posts: 1128
Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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14 Mar 2016, 19:08
3
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
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Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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30 Sep 2018, 11:25
1
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

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Joined: 04 Jan 2015
Posts: 2291
Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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30 Sep 2018, 15:09
1

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
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Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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30 Sep 2018, 19:43
1
Bunuel wrote:
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

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 $$\frac{d}{1.25s} = \frac{d-7}{s}$$

$$ds = 1.25ds - 8.75s$$

$$d = 1.25d - 8.75$$

$$d = \frac{8.75}{0.25} = 35$$.
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Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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01 Oct 2018, 05:08
Bunuel wrote:
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

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)
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VP
Joined: 09 Mar 2016
Posts: 1215
Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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01 Oct 2018, 12:21
Bunuel wrote:
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

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

$$(x-7)125 = 100x$$

$$125x-100x=875$$

$$25x=875$$

$$x = 35$$
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Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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03 Oct 2018, 16:38
Bunuel wrote:
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

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

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Intern
Joined: 29 Jul 2018
Posts: 6
Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to  [#permalink]

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12 Oct 2018, 06:05
1
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

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Re: A runs 25% faster than B and is able to allow B a lead of 7 meters to &nbs [#permalink] 12 Oct 2018, 06:05
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# A runs 25% faster than B and is able to allow B a lead of 7 meters to

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