Otherwise, I understand the math. Just wondering why they would ever meet outside the city.

This problem has driven me crazy for more than 1 hr now, I am trying to find what is the issue in my understanding..

Worst, I am getting 3 diff answers..
I assume total dist i.e. dist bet cities = D. Total time = 240 min. Constant speed for both buses = D/240.

RTD Chart

T R D
240 D/240 D
156 (i.e.120+36) D/240 (D/2) + 24 For bus leaving early, no need to care abt other bus
96 (i.e. 120-24) D/240 (D/2) - 24 For bus leaving late, no need to care abt other bus

1st Linear equation for D (bus leaving early):
(156D)/240 = (D/2) + 24=>D=160
2nd Linear equation for D (bus leaving late):
(96D)/240 = (D/2) - 24=>D=240
3rd case, same as tingle15 above:
( (D/2) + 24 ) /(D/240) - ( (D/2) - 24 ) /(D/240) = 156 - 96=>D=192 (OE).

Also, since speed is constant, even using simple direct proportion, we get D=160:
36->24
240->D
=>D=160

Can Bunuel/somebody pls explain the mistake here/if the no. 24 in the question should be changed..Worst, I hope there is no calculation mistake on my part..

Thanks.

Can someone help me with my flaw in logic please?

24minutes /60 minutes = .4 hours
36 minutes / 60 min = .6 hours

NOT .5!!

So, bus one (we'll call M) drove 1.6 hours to get to p-24
Bus two (bus N) drove 24 minutes + 36 minutes + the 1.6 hours that M was driving = 2.6 hours.

1.6*M = P - 24
2.6*N = P + 24
So, 2N = P and 2M = P...

2.6N - P - 24 = 2N - P yields: .6N = 24 > N = 40 mph

1.6M - P + 24 = 2M - P yields: 24 = .4M > M = 60 mph

2h * 60 mph = 120 miles (bus M)
2h * 40mph = 80 miles (bus N)

= 200 miles?

The biggest issue I am having is how they are getting 1.5, 2.5, etc. 36 minutes / 60 minutes = .6 hours not .5 HOURS!

Thanks!

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

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this was tricky....moreover it dosent look like a 600 level ques......Should have been 700+...

Or may be i am confused because of the wordings....
_________________

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