SIM Motion

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Sun Jun 14, 2009 2:42 pm

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

Abdulla

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Source: Beat The GMAT — Data Sufficiency | Sun Jun 14, 2009 2:42 pm

tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Sun Jun 14, 2009 10:49 pm

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.

The powers of two are bloody impolite!!

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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Sun Jun 14, 2009 10:51 pm

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

The powers of two are bloody impolite!!

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pg850: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Sat Jun 13, 2009 12:33 pm; Location: Mumbai, India

by pg850 » Sun Jun 14, 2009 11:49 pm

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

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

by Vemuri » Mon Jun 15, 2009 4:06 am

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.

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kumadil2011: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sat Nov 12, 2011 10:20 pm

by kumadil2011 » Wed Nov 30, 2011 9:09 am

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)

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Wed Nov 30, 2011 11:55 am

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

Just started my preparation

Want to do it right the first time.

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Thu Dec 01, 2011 9:29 am

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

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

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BestGMATEliza: Master | Next Rank: 500 Posts; Posts: 103; Joined: Mon Jun 23, 2014 11:31 pmFollowed by: 12 members; Thanked: 25 times; GMAT Score:770

by BestGMATEliza » Wed Jul 09, 2014 9:49 pm

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

Eliza Chute
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 10, 2014 4:05 am

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.

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