difficult math question # 102

iLdern wrote:Jane gave Karen a 5 m head start in a 100 race and Jane was beaten by 0.25m. In how many meters more would Jane have overtaken Karen?

Could someone please give a good explanation for this problem?

Thaaaanks

Hi!

First, please include the source and choices in your future posts. The choices often give lots of great hints as to how to attack the question.

Let's start by jotting down the distance equation:

distance = rate * time

or

t = d/r

Here, Karen ran 95m (she had a 5m head start) and Jane ran 99.75m. Their times are equal.

Since their times are equal, we know that:

99.75/rateJ = 95/rateK

rateJ/rateK = 99.75/95 = 21/20

So, for every 20 metres that K runs, J runs 21.

Over 20 metres, J gained 1 full metre. We only need J to gain 1/4 of a meter, so it will take 1/4 of 20 = 5 metres.

Now, the question is ambiguous, since K will run 5 metres and J will run 5.25 in that time. Overall, the question isn't very well worded (which is why it's important to provide the source).

Thanks for the explanation Stuart. However, did you mean rateJ/rateK = 19.75/19 ~ 20/19 ?

Thank you very much for the explanation - it really helped me understand the proper way to attack this problem.

As for the source, I copied the question from a document a user uploaded to this forum called "gmat MATH tough problems". This question was presented without answer choices.

The document provided a solution I didn't quite follow:
Soln: Jane gave Karen a 5 m head start means Karen was 5 m ahead of Jane. So after the lead, Karen ran 95m and Jane ran 99.75 m when the race ended.

Let speed of Karen and Jane be K and J respectively and lets say after X minutes Jane overtakes Karen.


1st condition: 95/K = 99.75/J


2nd condition JX - KX = 0.25


Solving for JX, we get JX=21/4.


Hence Jane needs to run 5.25m more (or total of 105m) to overtake Karen.


Again, Thank you very much for your explanation.

fc123 wrote:Thanks for the explanation Stuart. However, did you mean rateJ/rateK = 19.75/19 ~ 20/19 ?

Hi,

I think my math is correct.

Over the first part of the race, in the same amount of time, J ran 99.75m and K ran 95m. So, the ratio of their rates is:

99.75/95

= (95 + 4.75)/95

= 95/95 + 4.75/95

= 1 + 1/20

= 21/20

On another note, a second problem with this question is that nowhere does it say that J and K run at constant speeds - a fact that a real GMAT question would have to contain (since we can't assume that, for example, Karen doesn't put on a burst of speed near the end of the race).

Ok, I see that now. Thanks! I agree with you, the question seems incomplete rather.