Question 1017542
What is the 1st train's head start in miles?
Let {{{ s }}} = the speed of the 1st train in mi/hr
From 2PM to 4PM is 2 hrs
{{{ d[1] = s*2 }}}
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Let {{{ d }}} = distance the 2nd train travels until
it overtakes the 1st train
From 4PM to 6PM is 2 hrs
Start time when the 2nd train leaves
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Equation for 1st train:
(1) {{{ d - 2s = s*2 }}}
Equation for 2nd train:
(2) {{{ d = ( s+42 )*2 }}}
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Substitute (2) into (1)
(1) {{{ ( s+42 )*2 - 2s = s*2 }}}
(1) {{{ 2s + 84 - 2s = 2s }}}
(1) {{{ 2s = 84 }}}
(1) {{{ s = 42 }}}
and
{{{ s+ 42 = 42 + 42 }}}
{{{ s + 42 = 84 }}}
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The 1st train's speed is 42 mi/hr
The 2nd train's speed is 84 mi/hr
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check:
(2) {{{ d = ( s+42 )*2 }}}
(2) {{{ d =84*2 }}}
(2) {{{ d = 168 }}}
and
(1) {{{ d - 2s = s*2 }}}
(1) {{{ d - 2*42 = 42*2 }}}
(1) {{{ d = 84 + 84 }}}
(1) {{{ d = 168 }}}
OK