Data Sufficiency

Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

(A) R – 4

(B) R/R + 4

(C) R/R – 8

(D) 8/R – 8

(E) R^2 – 4

OA is C

just plugin any value for R
I plugged in 16 miles per hour
so in one hour
if Brenda take time t to cover twice the distance traveled by alex in t1 time
16t=2*4*t1
t1=2t
if t=1
t1=2
now use the answer options
A)R-4=12 no
B)R/R+4=16/20 no
C)R/R-8=16/16-8=2 yes
D)8/R-8=8/8=1 No
E)Nooo

of course if you get same values for two options you need to substitute some other values.

and by the way ..this question should go under the problem solving thread

Another way to solve the problem:

IF 'x' is the amount of time for Brenda to cover twice the distance of Alex,
then (4+4x)*2 = Rx [Equatinf the distance travelled by both]

Solving for x would give, x = 8/(R-8)

To find total time for Alex, add 1 to this giving you the answer,

R/(R-8)

-PG

If none of the above approaches click on the D day, just assume a value for R, i.e. R=9 & then check when the distance travelled by Brenda becomes double the value of Alex's distance.

Hr ---- Alex ---- Brenda
1 ---- 4 miles 0 miles
2 ---- 8 miles 9 miles
3 ---- 12 miles 18 miles
4 ---- 16 miles 27 miles
5 ---- 20 miles 36 miles
6 ---- 24 miles 45 miles
7 ---- 28 miles 54 miles
8 ---- 32 miles 63 miles
9 ---- 36 miles 72 miles

Plug in the value of R & you will get C as the answer.

Why cant i solve by following method

let time taken by Bre be T, and Alex be T+1..

I get the solution if i take T-1 for Bre and T for Alex..can some one guide me when to pick pair like (T and T+1) and (T and T-1)

kumadil2011 wrote:Why cant i solve by following method

let time taken by Bre be T, and Alex be T+1..

I get the solution if i take T-1 for Bre and T for Alex..can some one guide me when to pick pair like (T and T+1) and (T and T-1)

okay let B took T & A took T+1

so from question
distance travelled by A * 2 = distance travelled by B
=> 4(T+1)*2 = R*T
=> 8T+8 = RT
=> T(R-8) = 8
=> T = 8/(R-8)
since we need to tell the time from Alex's point of view, we need to find T+1 from above
=> T+1 = 8/(R-8) + 1
=> T+1 = R/(R-8)

hope this helps

user123321

4t=S
r(t-1)=2S

8t=r(t-1)
rt-8t=r
t=r/(r-8)

So lets make t= the time (in hours) that alex has walked. Then, the time Brenda has biked would be t-1, because she started an hour after alex.

We know that the Distance = Rate*Time, so we want to find the time when Brenda's Distance is twice that of Alex.

For Alex D=4t and for Brenda D=R(t-1), thus we are looking for when 8t=R(t-1)

let's multiply out the R, so 8t=Rt -R

now let's put all the ts on one side thus, 8t-Rt=-R

take out the t, so (8-R)t=-R

Now, divide both sides by (8-R) and we have t=-R/(8-R)

this exact equation isn't an answer choice, but we can multiply the top and the bottom of the fraction by -1 to get: R/(R-8), which is C

Abdulla wrote:Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?

(A) R - 4

(B) R/R + 4

(C) R/R - 8

(D) 8/R - 8

(E) R^2 - 4

Let R = 16mph.
We can PLUG IN THE ANSWERS, which represents Alex's time.

Answer choice C: R/(R-8) = 16/(16-8) = 2 hours.
At a rate of 4mph, the distance traveled by Alex in 2 hours = 4*2 = 8 miles.
Since Brenda starts to bike 1 hour after Alex starts to walk, Brenda bikes for 1 hour.
At a rate of 16mph, the distance traveled by Brenda in 1 hour = 16*1 = 16 miles.
Success!
Brenda's distance is twice Alex's distance.

The correct answer is C.