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2014-11-14T02:25:01+05:30

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See diagram.

let the bridge be L miles long.  Let Anoop run v miles per hour.

Hence by the time Anoop runs to EITHER END of the railroad bridge, the train just comes to the SAME end of the bridge.
 
1)  Anoop runs L - 5L/6 = L/6 distance,  to the nearer end of the bridge.
     The train has to run through the distance x.

\frac{L/6}{v} = \frac{x}{35}\ \ \ \ => \ \ v = \frac{35 L}{6 x}, \ \ \ - equation 1

2)  Anoop runs 5L/6 to the farther end of the bridge.

\frac{L+x}{35} = \frac{5L/6}{v},\ \ \ => \ v = \frac{35*5 L}{6 (L+x)}, \ - equation\ 2

   divide equation 2  by equation 1  =>
 1 = \frac{5 x}{L+x},\ \ => \ L + x = 5 x,\ \ \ L=4\ x,\ \ \ - equation3 

   
     substitute in equation 1,
 v = \frac{35 * 4 x}{6 * x} = \frac{140}{6} = 23.66 mph\\

Anoop can run at 23.66 mph


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