Question 1050579
In 2 hrs, the 1st train's head start is:
{{{ d[1] = 75*2 }}}
{{{ d[1] = 150 }}} mi
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Start a stopwatch when the 2nd train leaves
Let {{{ t }}} = time in hrs on the stopwatch when
they meet
Let {{{ d }}} = distance in miles the 2nd train
travels until they meet
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Equation for 1st train:
(1) {{{ d - 150 = 75t }}}
Equation for 2nd train:
(2) {{{ d = 125t }}}
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substitute (2) into (1)
(1) {{{ 125t - 150 = 75t }}}
(1) {{{ 50t = 150 }}}
(1) {{{ t = 3 }}} hrs
and
(2) {{{ d = 125t }}}
(2) {{{ d = 125*3 }}}
(2) {{{ d = 375 }}} mi
They will meet 375 mi from the station
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check:
(1) {{{ d - 150 = 75t }}}
(1) {{{ d - 150 = 75*3 }}}
(1) {{{ d = 225 + 150 }}}
(1) {{{ d = 375 }}}
OK