itsagulati wrote:
Sure.
Let's say 12p.m. is the scheduled departure...
Bus M was scheduled to leave at 12, but was delayed 24 min (.4 hours...24min / 60min). So, this left at 12:24 p.m.
Bus N was scheduled to leave at 12 p.m. as well, but left 36 minutes early at 11:24 a.m.
Bus N takes at LEAST 2 hours to get to point P. Thus, it cannot arrive before 1:24 p.m., however, we know that bus N travels farther since we are going past point P (or you can look at it as M can at best reach half way to point P since it has only been going for an hour at 1:24 p.m.). Thus, you go to 2 p.m. which is the original area they would have met at point P, but bus M is not to point P since delayed (it is 24 miles short) and bus N has been going longer than 2 hours which is how it gets to be P+24.lost you here
Let me know if that helps or further confuses..i realize that was incredibly wordy.
Also, in case that equation wasn't clear...
Bus M only gets to drive 1.6 hours (delayed 24 min, 24 min / 60 = .4, 2-.4 = 1.6 hours). And 36 min early departure + 24 min. the delay that bus N didn't experience = 1 hour extra that bus N gets to drive over bus M. Thus:
Bus M: 1.6x = P - 24 (24 miles shorter than point P) and...
Bus N: 2.6x = p + 24 (went 24 miles past point P in the 1 hour extra it had compared to bus M)
M leaves @ 12:24PM
N leaves @ 11:24AM
As you rightly said: N travels P/2 distance until 12:24PM, when M starts its journey.
Let's try to understand this using a line. Let the two extreme points be X and Y.
I. X(M)---------------------------P---------------------------(N)Y @11:24AM, where XP=YP
II. X(M)---------------------------P------------(N)R--------------Y @12:24PM, because N left early and covered half of YP; PR=RY=1/4*XY
III. X--------------------(M)(N)T-------P-------------R-------------Y @Some time after 1:24PM. The important thing to note here is that the point, let's call it T, where "MN" have met is again midway from X and R in the immediately previous line(II). Why? Because M and N travels with same constant speed.
PR+PT=XT [:Note: T is midway from X and R]
PR+24=XT
PR=1/2*PY=1/2*1/2*(XY) [:note: P is midway from X and Y]
XT=PR+24=1/4*XY+24 --------------------------1
Also,
XT=XY-TY=XY-(PY+PT)=XY-(1/2*XY+24)=1/2*XY-24---------------------2
Equate 1 and 2:
1/4*XY + 24 = 1/2*XY - 24
1/4*XY=48
XY=48*4=192
******************************************************
See it another way;
XT= 3/8*XY
M travels XY in 4 hours
M would travel 3/8*XY in (3/8)*4=1.5 hours
Thus, M and N meet 1.5 hours after M starts its journey i.e. @1:54PM
********************************************************
Please let me know if something is unclear.
_________________
~fluke
Find out what's new at GMAT Club - latest features and updates
close
