Question 446341
How much of a head start does the 1st train get?
{{{ d[1] = 30*.5 }}}
{{{ d[1] = 15 }}} mi.
Write equations for both with {{{t}}} equal to the time
from when the 2nd train leaves to when they meet,
and {{{d}}} = distance the 2nd train has to go to
where they meet
1st train:
(1) {{{ d - 15 = 30t }}}
2nd train:
(2) {{{ d = 50t }}}
------------
(1) {{{ d - 15 = 30t }}}
(1) {{{ d = 30t + 15 }}}
{{{ 30t + 15 = 50t }}}
{{{ 20t = 15 }}}
{{{ t = .75 }}}
{{{ t + .5 = 1.25 }}}
They will meet 45 minutes after the 2nd train leaves
and  1 hour 15 minutes after 1st train leaves
check:
(1) {{{ d - 15 = 30t }}}
(1) {{{ d - 15 = 30*.75 }}}
(1) {{{ d = 15 + 22.5 }}}
(1) {{{ d = 37.5 }}}
and
(2) {{{ d = 50t }}}
(2) {{{ d = 50*.75 }}}
(2) {{{ d = 37.5 }}}
OK