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04 Dec 2019, 02:14
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
38% (03:14) correct
62%
(03:03)
wrong
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Rebecca runs at a constant rate on the treadmill and it takes her 2 hours longer to reach a certain milestone than the time it takes Jeff to reach that same milestone. If Jeff also moves at a constant rate and the two are allowed to combine their distances traveled to reach 25% beyond the initial milestone in 3 hours, how many hours would it take for Rebecca alone to reach the equivalent distance of 2 milestones?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Are You Up For the Challenge: 700 Level Questions
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Are You Up For the Challenge: 700 Level Questions
04 Dec 2019, 05:24
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Time taken by Rebecca to reach 1 milestone= T(R)
Time taken by Jeff to reach 1 milestone= T(J)
Time taken by both= T(R+J)
T(R+J)= 3*4/5= 2.4 Hours
As T(R)>T(J)> T(R+J), Eliminate option A, B and C
Option D
T(R+J)= \(\frac{3*5}{8}\)=\(\frac{15}{8}\) < 2.4
Eliminate it
Option E
T(R+J)= \(\frac{4*6}{10}\)= 2.4 (Answer)
Time taken by Jeff to reach 1 milestone= T(J)
Time taken by both= T(R+J)
T(R+J)= 3*4/5= 2.4 Hours
As T(R)>T(J)> T(R+J), Eliminate option A, B and C
Option D
T(R+J)= \(\frac{3*5}{8}\)=\(\frac{15}{8}\) < 2.4
Eliminate it
Option E
T(R+J)= \(\frac{4*6}{10}\)= 2.4 (Answer)
Bunuel
07 Dec 2019, 22:53
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Let the time taken by Rebecca(R) to complete 1 milestone (MS) be T hours. Then Jeff(J) takes (T-2) hours to complete 1 MS.
In 3 hrs, R completes 3/T MS and J completes 3/(T-2) MS so the sum of the distances covered by each in 3 hrs is: [3/T+3/(T-2)] hrs which is equal to
1.25 MS. Therefore:
3/T+3/(T-2)=5/4....> 5T(T-6)-4(T-6)=0....> (5T-4)(T-6)=0. So T is equal to 4/5 or 6. Since Jeff takes 2 hrs less than Rebecca to complete 1 MS, T cannot be 4/5 hrs because that would give a negative value for Jeff's time. So T=6 which means R will take 6*2=12 hrs to complete 2 MS.
ANS: E
In 3 hrs, R completes 3/T MS and J completes 3/(T-2) MS so the sum of the distances covered by each in 3 hrs is: [3/T+3/(T-2)] hrs which is equal to
1.25 MS. Therefore:
3/T+3/(T-2)=5/4....> 5T(T-6)-4(T-6)=0....> (5T-4)(T-6)=0. So T is equal to 4/5 or 6. Since Jeff takes 2 hrs less than Rebecca to complete 1 MS, T cannot be 4/5 hrs because that would give a negative value for Jeff's time. So T=6 which means R will take 6*2=12 hrs to complete 2 MS.
ANS: E
