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# A and B ran, at their respective constant rates, a race of 480 m. In

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Manager
Joined: 05 Jul 2006
Posts: 192
A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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16 Nov 2006, 08:36
1
3
00:00

Difficulty:

65% (hard)

Question Stats:

70% (01:40) correct 30% (03:26) wrong based on 43 sessions

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A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

OPEN DISCUSSION OF THIS QUESTION IS HERE: speed-time-problems-106921.html
Manager
Joined: 29 Aug 2006
Posts: 155
Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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16 Nov 2006, 08:58
1
1
I get A.

Time taken by A=t1
Time taken by B=t2
A-speed of A
B-speed of B
1/10th of a minute =60/10=6seconds
1/30th of a minute= 2seconds

For first heat,
t1=480/A
t2=(480-48)/B
and t1=t2-6

For second heat,
t1=480/A
t2=(480-144)/B
t1=t2+2

hence
480/A= 432/B - 6
and
480/A=336/B + 2

Using both equations,
336A+2AB=432A-6AB
8B=96
B=12

Is this the right answer and does anybody know a shortcut?...it took me more than 2 mins to answer this one.
Director
Joined: 02 Mar 2006
Posts: 535
Location: France
Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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16 Nov 2006, 09:22
1
1
I did it like that :

144-48 = 96 m is the distance B runs in 1/10 - 1/20 minutes.

=> 96 m in 8 s

=>96/8 =12 m/s

A.
SVP
Joined: 24 Aug 2006
Posts: 2090
Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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16 Nov 2006, 11:27
1
lan583 wrote:
6. A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is Bâ€™s speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

let B = B's speed
let Z = total distance
let x = time in seconds

heat1 B(x+6)=Z-48
heat2 B(x-2)=Z-144

B(x+6)+48=Z B(x-2)+144=Z

B(x+6)+48=B(x-2)+144

solve

B=12
Senior Manager
Joined: 20 Feb 2006
Posts: 367
Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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16 Nov 2006, 14:17
time = distance/speed

1) For first race: Time for B - Time for A = 6s

2) For second race: Time for B - Time for A = - 2s (A is beaten in this race)

Plugging into those equations

1) 432/speed B - 480/speed A = 6

2) 336/speed B - 480/speed A = -2

Now 1) - 2) ---------> 96/B = 8 or 8B = 96 or B=12
Math Expert
Joined: 02 Sep 2009
Posts: 52161
Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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10 Jan 2015, 04:48
lan583 wrote:
A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B’s speed in m/s?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

Let $$x$$ be the speed of B.

Write the equation:

(480-48)/x (time of B for first heat) - 6 (seconds, time B lost to A first heat) = TIME OF A (in both heats A runs with constant rate, so the time for first and second heats are the same)=(480-144)/x (time of B for second heat) + 2 (seconds, time B won to A second heat)

$$\frac{480-48}{x}-6=\frac{480-144}{x}+2$$ --> $$x=12$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: speed-time-problems-106921.html
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Joined: 09 Sep 2013
Posts: 9415
Re: A and B ran, at their respective constant rates, a race of 480 m. In  [#permalink]

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20 Dec 2018, 01:55
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Re: A and B ran, at their respective constant rates, a race of 480 m. In &nbs [#permalink] 20 Dec 2018, 01:55
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