ravi007shankar 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 R2 – 4
Solution - Lets assume Alex travels X miles when Brenda begins to ride. Then,
Time taken by Alex = Time taken by Brenda
X/4 = [(X+4)2]/R --- since Brenda covers twice as distance as Alex in total thus Brenda distance is (X+4)2
which gives X = 32/(R-8)
Now time taken by Alex = X/4 = [32/(R-8)]/4 = 8/(R-8)
WHERE DID I GO WRONG ? Answer is C, not D
the wording is indeed confusing...and one might get messy with all the VIC's...
My approach, assign variables:
we need to find the time of A, when B covered twice the distance A covered.
since R>8, suppose R=9.
when alex covered 4 miles, brenda covered 0 - 1hour
when alex covered 8 miles, brenda - 9 miles - 2 hours
when alex covered 12 miles, brenda - 18 miles - 3 hours
when alex covered 16 miles, brenda covered - 27 miles - 4 hours
when alex covered 20 miles, brenda - 36 miles - 5 hours
when alex covered 24 miles, brenda - 45 miles - 6 hours
when alex covered 28 miles, brenda - 54 miles - 7 hours
when alex covered 32 miles, brenda - 63 miles - 8 hours
when alex covered 36 miles, brenda - 72 miles - AHA, we have 2X the distance. time - 9 hours.
ok, so when R=9, time must be 9.
now plug in values:
A R – 4 = 9-4=5 - out
B R / (R + 4) - 9/13 - out
C R / (R – 8) = 9/1 = 9 works, let's see other options
D 8 / (R – 8) = 8/-1 = -8
E R2 – 4 = 18-4=14 - nope.
C alone works. thus, C is the answer.
p.s. I see Rich is more experienced with testing values..he picked the numbers way better than me, and saved a lot of time