Question 420918
Start a stopwatch when train B leaves station at 3:22
How much of a head start does train A have?
Train A left 12 minutes earlier at 3:10, and at 40 mi/hr
{{{d = 40*(12/60)}}}
{{{d = 40/5}}}
{{{d = 8}}} mi is A's head start
Both trains will now run for the same amount of time,
but A has less distance to travel.
Let {{{d}}} = distance from station to where they meet
------------------
Train A:
(1) {{{ d - 8 = 40*t }}}
Train B:
(2) {{{d = 60*t }}}
-------------
(1) {{{ d = 40t + 8 }}}
(2) {{{ d = 60t }}}
{{{ 40t + 8 = 60t }}}
{{{ 20t = 8 }}}
{{{ t = 2/5 }}} hrs
{{{t = (2/5)*60}}} min
{{{ t = 24 }}} min
This is 24 minutes after the stopwatch started at 3:22,
so B catches A at 3:46 AM