Florence and Jackie are running laps on a circular quarter-mile track.

Question

Florence and Jackie are running laps on a circular quarter-mile track. If Florence completes each lap in 75 seconds and Jackie completes each lap in 90 seconds, how many laps will Jackie have run before she’s passed by Florence, assuming they start at the same time.

A. 5
B. 6
C. 7
D. 8
E. 9

A. 5
B. 6
C. 7
D. 8
E. 9

mcmoorthy · Accepted Answer

Thanks Luckisnoexcuse.

I calculated the LCM of 75 and 90 which will determine the point at which they meet.. LCM is 450.

Now Jackie would have run 450/90 which is 5 laps.

Hope this helps.

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Luckisnoexcuse · Answer

Lap 1 of J= 15 seconds behind F (J at start point)
Lap 2 = 30 s(J at start point)
Lap 3 = 45 s(J at start point)
Lap 4 = 60 s(J at start point)
Lap 5 = 75 s(J at start point) Here both are at starting point and F had completed 6 rounds
B

mcmoorthy · Answer

Hi Luckisnoexcuse,

The question is asking how many rounds Jackie has run and not Florence. Iam getting A as the answer. Can u pls clarify.

Thanks

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Luckisnoexcuse · Answer

mcmoorthy  ..ohh i missed it will be A (Jackie had run 5 rounds and florence 6)

Although i feel their is a much shorter version to solve as well (my instincts shouting) so waiting for others to solve

Klarbeinstreiter · Answer

Every round Florence needs 15 seconds less than Jackie (90-75). 
That means after 90/15 = 6 rounds Florence ran one more round than Jackie. 
At this point Jackie ran 5 rounds and Florence 6.

Answer A

Alternatively a table can be created and we keep adding the individual times until the time elapsed for Jacky and Florence are the same

--------Jacky------Florence Round
Time:----0------------0--------0
----------90----------75---------1
---------180---------150--------2
---------270---------225--------3
---------360---------300--------4
---------  450  ---------375--------  5  
---------540---------  450  --------  6

450 seconds were needed for Jacky to complete 5 rounds while Florence completed 6 rounds in 450 seconds.

Answer A

gracie · Answer

in 75 seconds F runs 1 lap
in 75 seconds J runs 75/90, or 5/6, of 1 lap
F runs 6 laps to J's 5 laps
5
A

felix89 · Answer

Another way i found using the classic (speed/time/distance) matrix would be:

Speed || Time || Distance
 F 75 || T || 75T+75 (# of laps with the extra lap needed)
 J 90 || T || 90T (# of laps)

If we equal 75T+75=90T
we find that T=5 which means that after 5 laps the total distance traveled by jackie is going to be equal to the distance traveled by florece + the additional lap. We can prove this by plugin in the results 75(5)+74=450=90(15)

bumpbot · Answer

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Florence and Jackie are running laps on a circular quarter-mile track.

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Florence and Jackie are running laps on a circular quarter-mile track.

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