Wednesday, December 28, 2011

Pnom Penh River Side View and the train problem


 Technically this is my 1st day in Pnom Penh. We arrived here yesterday evening. I slept a lot and infact was even late for shower. At 16:30 I decided its enough and I should go and explore the town. I am living on 63rd street and Raj showed me on the map its location with respect to the river side. Its not too far so I decided to amble my way to the river side. So the pictures are mainly from the river front, I had a delicious spiced up corn and spent some time going over review of things I wanted to do. Today I did find the solution to a trivial problem about a train passing two guys in 10 sec and 9 sec respectively. If the train takes 20 minutes to pass by the 2nd guy after it has completely passed the first guy. How long will it take for the first guy to overtake the 2nd one. I have the solution though its not the most elegant as I have relied on algebra. Mine solution goes like this
  Let the speed of train be v m/s
             speed of first person be x m/s
             speed of 2nd person be y m/s
let L be the length of the train in meters so we have the following two equations
L = (v-x) 10
L = (v-y) 9
which gives
10v -10x = 9v-9y
v = 10x-9y
Since it takes 20 minutes for the train to reach the second guy, let the distance between the front of the train and the person be M meters
Let after t sec they meet, during that t seconds
v (20*60) = M+x (20x60)
M = (v-x)(20x60) meters
The first person travels L+M+yT distance to catch y in time T, therefore
xT = L+M+yT
substituting for M and L we have
xT = (v-x)10+(v-x)(20x60)+yT
(x-y)T=(v-x)(10+20x60)
(x-y)T=(v-x)(10+1200)
Substituting for v we have
(x-y)T = (10x-9y-x)(1210)
(x-y)T =(9x-9y)(1210)
(x-y)T =9(x-y)(1210)
or T = 9(1210) seconds
which means T = 9x1210/3600 hrs






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