Rate problem

[varunsaini06]

Jane gave Karen a 5 m head start in a 100 m race and was beaten by 0.25m. In how many meters more would Jane have overtaken Karen?
a) 5m
b) 7m
C) 4.5m
d) 5.25m
e) 6m

Please let me knoe the answer.

Thanks,
Varun
http://varunsaini06.blogspot.com/

[nitin_prakash_khanna]

You will have to confirm to the forum that this is a GMAT prep problem or it should be moved to general maths forum.

In my view the answer is D (5.25m).

Let jane's speed be j mtr / sec and karen's k mtr/sec

since K has 5m head start and also won the race, K covered 95mtr while J covered 99.75mtr .

Which tells that
99.75 / j = 95 / k
j = 1.05 k

now this only tells that how fast j runs compared to k.

Now lets say that j overtakes k after t secs when they started.
so distance covered by k = k*t
distance covered by j = j*t

now we also know
j*t = 5+k*t (for 5 mtr of head start which k got)
1.05 k*t = 5+ k*t
0.05 k*t = 5
k*t = 100
if you realize k*t = distance travelled by k when j catches up so at 105 mtr from start mark j will catch up.

at finish line of 100 mtr, j was 0.25 mtr behind , so j has to run another 5.25 mtr before overtaking k.

A bit long method :>

[nile_sap]

Jane gave Karen a 5 m head start in a 100 m race and was beaten by 0.25m. In how many meters more would Jane have overtaken Karen?
a) 5m
b) 7m
C) 4.5m
d) 5.25m
e) 6m

Karen ran 95 m - Jane ran 99.75 m (100-0.25) in same time .
i.e Jane gained 4.75m over Karen when Jane ran 99.75m.
Therefore, to gain 0.25m (distance by which she lost the race), Jane will have to run: (0.25/4.75)*99.75=5.25m

[nitin_prakash_khanna]

thanks for a neat & quick method to approach this type of problem.

[tomslawsky]

This question can not be answered because the rates are not specified, or evenwher the rates are constant. What if the loser accelerated during the last few meters? Shame on the ETS for allowing a question with incomplete info make its way to an exam.

[RonPurewal]

This question can not be answered because the rates are not specified, or evenwher the rates are constant. What if the loser accelerated during the last few meters? Shame on the ETS for allowing a question with incomplete info make its way to an exam.

it's highly unlikely that this is an official problem.

it's not a bad problem, so we can leave it up here. but, yes, you are correct that the gmac people would absolutely specify those sorts of things.

or, worse, they'd put it in a data sufficiency problem whose answer is (e), precisely because you don't know those things. heh.