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A and B ran, at their respective constant rates, a race [#permalink]
26 Dec 2010, 07:47

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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

Re: Speed & Time Problems [#permalink]
26 Dec 2010, 08:08

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Expert's post

surendar26 wrote:

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 1/10 th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30 th of a minute. What is B’s speed in m/s?

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)

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 B’s speed in m/s?

what does giving head start mean in this question???? _________________

First of all, a "head start" is a term used frequently in American pop culture. If I have a "head start" in a race, that means that, for whatever reason, I have been given permission to walk beyond the starting line and start out already at a certain distance into the race. Suppose the race is from the 0 meters mark to the 100 meters mark. The standard participants will start at 0 meters and end at 100 meters. If I am given a "head start", I am allowed to start, say, at the 20 meter mark, and during the race, I have to run only from 20 meters to 100 meters. In other words, it's an advantage given to me, usually because I am perceived as being less able to compete well on my own. It's similar to the idea of a "handicap" in a sport like golf -- you can read more about that here: http://en.wikipedia.org/wiki/Handicapping

So, in the question you describe: In the first heat, A runs the full 480 meter, and B (with a head start of 48 m) runs a total distance of 480 - 48 = 432 meters. In that heat, A beat B by 1/10 of a minute, i.e. 6 seconds. It took B six seconds longer to finish.

In the second heat, A runs the full 480 m, and B (now with a head start of 144 m) runs a total distance of 480 - 144 = 336 meters. In that heat, B beat A by 1/30 of a minute, i.e. 2 seconds. It took B 2 seconds fewer to finish.

D = RT, so T = D/R

We will let t be the time it takes A to run the 480. Let vA be A's speed, and vB be B's speed. Then, we have

(1) t = 480/vA

(2) t + 6 = 432/vB

(3) t - 2 = 336/vB

Subtract equation (3) from equation (2), and we are left with: 8 = 96/vB --> 8vB = 96 ---> vB = 12 m/s

Does that make sense? Please let me know if you have any questions.

Mike _________________

Mike McGarry Magoosh Test Prep

Last edited by mikemcgarry on 11 Jan 2012, 08:44, edited 2 times in total.

We will let t be the time it takes A to run the 480. Let vA be A's speed, and vB be B's speed. Then, we have

(1) t = 480/vA

(2) t + 6 = 432/vB

(3) t + 2 = 336/vB

Mike, I think the 3rd equation should be t-2 =336/vB, because it is stated in the question that A got beaten by B. So according to that the answer should come out to be 12m/s.

Re: A and B ran, at their respective constant rates, a race [#permalink]
24 Feb 2012, 09:09

surendar26 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

Hi!

B ran 96m less in second heat (144-48), which allowed him to “gain back” 8 seconds (from 6 loss to 2 seconds win). So, 96/8 = 12m/s.

Re: A and B ran, at their respective constant rates, a race [#permalink]
19 Apr 2013, 02:39

Expert's post

captainhunchy 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

I initially solved the equation like this and got the wrong answer, but don't know why??

Time of B (heat 1) = (480+48)/A + 6 ; where A = rate of A Time of B (heat 2) = (480+144)/A - 2

Since B's time is constant in both heats I will set them equal to each other.

(480+48)/A + 6 = (480+144)/A -2

528/A + 6 = 624/A -2 A = 12m/s

I know this is wrong because, this means B's rate can't be 12ms... But I don't get why the equation is wrong.

In the first heat B covers 480-48=432 meters and in the second heat B covers 480-144=336 meters, thus the times of B in two heats cannot be the same. In both heats A runs 480 meters, so the times of A in two heats are the same.

Re: A and B ran, at their respective constant rates, a race [#permalink]
19 Apr 2013, 10:47

Experts a question for you.. I am aiming for 650+ score and quant is an area i can improve on.. What should be an ideal time for solving a question like this. I am at currently around 2m 45 secs. _________________

You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

Re: A and B ran, at their respective constant rates, a race [#permalink]
25 Jun 2014, 10:04

How can you add or subtract time to a rate. Based on the explanation you are equating the two rates of B but you are also subtracting 6 seconds from the rate and adding 2 seconds to the rate. I am looking at this through the D = RT formula and don't know how you can do R = (D/T) - 6.

Appreciate the help.

Bunuel wrote:

surendar26 wrote:

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 1/10 th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30 th of a minute. What is B’s speed in m/s?

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)

Re: A and B ran, at their respective constant rates, a race [#permalink]
25 Jun 2014, 14:15

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In first case, B was given 48m headstart and he by 6 seconds. (1/10th of a minute) In the second case, B was given head start of 144m and he wins by 2 sec (1/30th of a minute)

Hence we know this time difference of 8 seconds (from loosing by 6 sec to winning by 2 seconds), is due to the fact that B travelled 144-48 = 96m more in first case. Now B travelled this 96m in 8 sec and hence, speed of B = 96/8 = 12m/s

Am I correct by approaching the problem this way or is there any thing I missed ?

Re: A and B ran, at their respective constant rates, a race [#permalink]
25 Jun 2014, 15:33

Time taken by A in both the cases are the same. In the first case it is 6 seconds less than that of B and in the second case it is 2 seconds more than that of B.