Question 1076973
Find the head start in miles for the 1st train
{{{ d[1] = 50*5 }}}
{{{ d[1] = 250 }}} mi
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Let {{{ d }}} = distance in miles the 2nd train
travels until they meet
Let {{{ t }}} = time in hrs after 2nd train leaves
until they meet
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Equation for 1st train:
(1) {{{ d - 250 = 50t }}}
Equation for 2nd train:
(2) {{{ d = 175t }}}
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Plug (2) into (1)
(1) {{{ 175t - 250 = 50t }}}
(1) {{{ 125t = 250 }}}
(1) {{{ t = 2 }}}
and
(2) {{{ d = 175t }}}
(2) {{{ d = 175*2 }}}
(2) {{{ d = 350 }}}
They will meet 350 mi from the station
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check:
(1) {{{ d - 250 = 50t }}}
(1) {{{ d - 250 = 50*2 }}}
(1) {{{ d = 250 + 100 }}}
(1) {{{ d = 350 }}}
OK