Question 1091996
The head start of the freight train in miles is:
{{{ d[1] = 50*4 }}}
{{{ d[1] = 200 }}} mi
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Start a stopwatch when the passenger train leaves. 
Let {{{ t }}} = time in hrs on the stopwatch when the
passenger train catches up with the freight train
Let {{{ d }}} = distance in miles the passenger train 
travels until it catches up with the freight train
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Equation for the pasenger train:
(1) {{{ d = 90t }}}
Equation for the freight train:
(2) {{{ d - 200 = 50t }}}
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Plug (1) into (2)
(2) {{{ 90t - 200 = 50t }}}
(2) {{{ 40t = 200 }}}
(2) {{{ t = 5 }}}
The passenger train will catch the freight train in 5 hrs
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check:
(1) {{{ d = 90*5 }}}
(1) {{{ d = 450 }}}
and
(2) {{{ d - 200 = 50*5 }}}
(2) {{{ d = 200 + 250 }}}
(2) {{{ d = 450 }}}
OK