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# In a 1000 m race, A gives B a start of 40 m and beats him by

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Manager
Joined: 28 Jun 2004
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In a 1000 m race, A gives B a start of 40 m and beats him by [#permalink]

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17 Aug 2004, 19:02
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In a 1000 m race, A gives B a start of 40 m and beats him by 19 seconds. If A gives B a start of 30 seconds, B beats A by 40 m. Find the ratio of their respective speeds.

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17 Aug 2004, 20:42
Not sure if I'm right working out this way, my gut feeling is I'm wrong as the ratio has a crazy number. But here it is.. if its' wrong, will be glad to see the solution !

Let A and B be the speed of A and B respectively. Then

1000/A - 960/B = 19 secs (From statement 1)

1040/B - 1000/A = 30 secs (From statement 2)

So solving gives B = 80/49 meters per second
and A = 1000/607 meters per second

So the ratio A/B = 1225:1214

I think I'm definitely wrong, but that's how I interprete the statements.

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Director
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17 Aug 2004, 22:16

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18 Aug 2004, 00:39
Venksune, i think your post has some error in it? Do you mind posting it again ?

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GMAT Club Legend
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18 Aug 2004, 02:03
Hey Venksune, do you think you can explain how you derived both your equations ? thanks in advance !

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Manager
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18 Aug 2004, 06:23
ywilfred wrote:
Not sure if I'm right working out this way, my gut feeling is I'm wrong as the ratio has a crazy number. But here it is.. if its' wrong, will be glad to see the solution !

Let A and B be the speed of A and B respectively. Then

1000/A - 960/B = 19 secs (From statement 1)

1040/B - 1000/A = 30 secs (From statement 2)

So solving gives B = 80/49 meters per second
and A = 1000/607 meters per second

So the ratio A/B = 1225:1214

I think I'm definitely wrong, but that's how I interprete the statements.

From 1st fact, when A travels 1000 m, B manages to travel only 1000-40=960m. Also, B gets beaten by 19 seconds. Hence, B travels MORE by 19 seconds compared to A's time.

So you get, (1000/v1) = (960/v2) - 19 (you have to take out 19, rather than add 19 to balance the equation, as B's time is more).

From the second fact, you get, (960/v1) = (1000/v2) - 30 (Here again we take out 30 seconds, as B travels MORE by 30 seconds).

You really cannot use 1040 in the second equation, as it will mess up your time ratio. A does not travel more than the length of the race.

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18 Aug 2004, 06:29
But if B is beaten by 19 seconds, that means when A reaches the finishing line, B is still 19 seconds behind. So 19 seconds should be added if we want to equate both sides, shouldn't we?

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Manager
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18 Aug 2004, 06:33
ywilfred wrote:
But if B is beaten by 19 seconds, that means when A reaches the finishing line, B is still 19 seconds behind. So 19 seconds should be added if we want to equate both sides, shouldn't we?

The way I understand it is, if X beats Y by 19 seconds, that means that X is faster and Y is slower. Hence X reaches finishing line in less than (19 seconds) than Y. That means that Y will still travel 19 MORE seconds after X has already reached the finishing line. So if you are comparing time, you need to take out 19 seconds from the slower guy to equal them up.

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Manager
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18 Aug 2004, 06:41
If you look at the statement "In a 1000 m race, A gives B a start of 40 m and beats him by 19 seconds". That means that A has beaten B in the race. That means that both A and B NEED TO COMPLETE the race if one of them has to be beaten.

If I am not wrong, your interpretation of the statement is, at the time when A reaches finishing line, B is "19 seconds behind A" and race is over. But if you interpret it like that, that means that B still has not completed the race. If B has not completed the race yet, he cannot be beaten. He can only be beaten when he actually completes the race (atleast in our situation )

Any flaws you see?

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18 Aug 2004, 07:10
That's exactly how i interpreted the question ! I suppose we can't assume too much when we deal with these questions ! This one will go into my notebook

Thanks for the explanation !

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Manager
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18 Aug 2004, 07:16
I really thought about this, and this is the conclusion I came to. If A beats B in time, than we need to take time out of B to equal their TIMES. Alternatively, if A beats B is distance, than we need to add distance to B to equal their DISTANCES.

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18 Aug 2004, 07:21
That's a really interesting way to look at it. I got a little confused when the question started going into how much time B is beaten. I just kept thinking whether to add or not. I guess this method is a great way to remember !

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Director
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18 Aug 2004, 08:11
Sorry guys to chip in late...I think you guys had some great discussions and I can see that there is already enough understanding now.

I can add some good race / time-dsitance problems....do u guys wanna try it. Let me know...and I will post them.

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18 Aug 2004, 08:42
Venksune, I'm all game for these questions ! I need to sharpen my abilities a little at these problems. Keep them coming !

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18 Aug 2004, 08:42
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