Rebecca runs at a constant rate on the treadmill and it takes her 2 ho

Question

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

nick1816 · Answer

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)

effatara · Answer

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:   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

aarushisingla · Answer

3/T+3/(T-2)=5/4

Why the speed is not included in the formula ?

Yellowp · Answer

Hi Bunuel, would you please release an official solution for this one? Tried to understand other's explanation but still very lost.. thanks!

KeyurJoshi · Answer

IMHO  E  
Idk how much correct I was when arriving at the solution, still lost a little.

Let the time taken for Jeff = t
Let the time taken for Rebecca = t+2
Distance till first milestone be = 100km
 
Distance ___________100km___________ | __25km__ | __25km__ | __25km__ |
 
Jeff ---------------t hrs-------------------|---t+3 hrs--|---t+6 hrs--|--t+9 hrs----|
Rebecca ---------------t+2 hrs----------------|---t+5 hrs--|---t+8 hrs--|--t+11 hrs----|

Eliminate a,b,c,d for t for rebecca > 11

chetan2u · Answer

The first method would be to make use of choices..

The choices give us time of R to cover 2 milestone, so half of each choice will give us time taken by R to cover 1 milestone, and THAT half -2 will give us time taken by J..

(A) 4
So R takes 4/2 or 2 hrs and J takes 2-2 =0...NOT possible

(B) 6
So R takes 6/2 or 3 hrs and J takes 3-2 =1, so J alone will cover 3/3 or 3 milestones in 3 hrs, but we are looking a combined distance of 1.25 milestone in 3 hrs...NOT possible

(C) 8
So R takes 8/2 or 4 hrs and J takes 4-2 =2, so J alone will cover 3/2 or 1.5 milestones in 3 hrs, but we are looking a combined distance of 1.25 milestone in 3 hrs...NOT possible

(D) 10
So R takes 10/2 or 5 hrs and J takes 5-2 =3, so J alone will cover 1 milestones in 3 hrs and R will cover 3/5 or 0.6 milestones. Combined they cover 1.6, but we are looking a combined distance of 1.25 milestone in 3 hrs...NOT possible

(E) 12
Only choice left, so our answer, but let us check
So R takes 12/2 or 6 hrs and J takes 6-2 =4, so J alone will cover 3/4 or 0.75 milestones in 3 hrs and R will cover 3/6 or 0.5 milestones in 3 hrs. Combined they cover 0.75+0.5=1.25 milestones..... Our answer

E

chetan2u · Answer

Second method could be..

R takes R hrs for 1 milestone, so in 3 hours, distance covered will be 3/R milestone
Similarly J will take R-2 hrs for 1 milestone, so in 3 hours, distance covered will be 3/(R-2) milestone
These 2 should equal 1.25 milestone.

So,  \frac{3}{R}+\frac{3}{R-2}=1.25=\frac{5}{4}..............................\frac{3R-6+3R}{R(R-2)}=\frac{5}{4} 
=>  4*6(r-1)=5*R(R-2) 
Either use choices to see.....E gives R as 12/2=6..... 4*6*(6-1)=5*6*(6-2).........4*6*5=5*6*4 ..YES
OR solve further
 24R-24=5R^2-10R...........5R^2-34R+24=0.....5R^2-30R-4R+24=0.....(R-6)(5R-4)=0 
So, R can be 6 or 4/5, but R cannot be 4/5 as J will become negative then..
Thus R=6, and twice of R or 12 hrs is required to cover 2 milestones..

E

ShankSouljaBoi · Answer

Let t be the time taken by Jeff to complete first milestone. J be jeff's speed and R be Rebeca's speed

jt = R(t+2) = d = firs ilestone distance

in 3 hrs,

3j + 3R = 1.25(R )

on solving t = 4 hrs
therefore, rebecca's time to complete one milestone is 6 hrs. Hence, to complete twice the milestone time taken by her would be
6*2 hrs = 12 ---> E

KarishmaB · Answer

Start with what you have so that need for variables is limited.

Together they reach 25% beyond milestone in 3 hrs. 
Ratio of 25% beyond milestone distance : milestone distance = 5 : 4
Ratio of time taken to reach 25% beyond milestone : time taken to reach milestone = 5 : 4 = 3 : ??
Time taken to reach the milestone together = 4*3/5 = 12/5 hrs

Let t be the time taken by Jeff alone to reach the milestone. Their rates are additive. 
1/t + 1/(t+2) = 5/12
t = 4 (No calculations needed. To get LCM 12, the denominators would be 3 and 4 or 4 and 6 or 2 and 12 ... look for the pair that has a difference of 2)

Rebecca takes 6 hrs for one milestone so she takes 12 hrs for 2 milestones

Answer (E)

sanjitscorps18 · Answer

Let the milestone distance be D
Let Rebecca's speed be R
Let Jeff's speed be J
Let the time taken by Jeff be T
Now D = R(T+2) = J(T)
Similarly as per the other statement both combine to make 1.25 D in 3 hours
=> 3R + 3J = 1.25 D
=> 3R + 3D/T = 1.25D
=> 3R = 1.25D - 3D/T
=> 3R = D(1.25T - 3)/T
=> 3RT = R(T+2)(1.25T - 3)
=> 3T = (T+2)(1.25T - 3)
=> 3T = 1.25T^2 - 3T + 2.5T - 6
=> 1.25T^2 - 3.5T - 6 = 0
=> 5T^2 - 14T - 24 = 0
=> (5T + 6)(T - 4) = 0

Now T cannot be negative hence T = 4
Now Rebecca takes T+2 = 6 hours 1 milestone
For 2 milestones Rebecca would take 6 * 2 = 12 hours

Option E

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Rebecca runs at a constant rate on the treadmill and it takes her 2 ho

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