Question 625091
Let {{{ d }}} = the distance between the cities
Let {{{ r[1] }}} = the rate of the Karnataka Express
Let {{{ r[2] }}} = the rate of the Kurla express
How much of a head start does the Karnataka Express have?
from 5 PM to 7 PM
{{{ d[h] = r[1]*2 }}} ( any units for d[h] )
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{{{ r[1] = d/4 }}}
{{{ r[2] = d/3.5 }}} ( any units for d - same as d[h] )
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Start a stopwatch when the Kurla Express leaves. They will both
travel for the same time, {{{ t }}}
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Think of one train as standing still, and the other approaching
at the sum of their speeds. The moving train must cover 
{{{ d - 2r[1]  = d - 2*(d/4) }}}
The sum of their speeds is:
{{{ d/4 + d/3.5 }}}
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{{{ 2*( d/4 ) = ( d/4 + d/3.5 )*t }}}
{{{ d/2 = d*( 1/4 + 1/3.5 )*t }}}
Divide both sides by {{{ d }}}
{{{ 1/2 = ( 1/4 + 2/7 )*t }}}
Multiply both sides by {{{ 28 }}}
{{{ 14 = ( 7 + 8 )*t }}}
{{{ t = 14/15 }}} hrs
{{{ 14/15*60 = 56 }}} minutes
They will meet at 56 minutes past 7
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check:
{{{ 2*( d/4 ) = ( d/4 + d/3.5 )*(14/15) }}} 
{{{ 15/2 = 14/4 + 14/3.5 }}}
{{{ 15/2 = 7/2 + 8/2 }}}
{{{ 15/2 = 15/2 }}}
OK