Question 1070826
3 PM to 4 PM is 1 hr
In 1 hr, the NY to BOS train travels
{{{ d[1] = 45*1 }}}
{{{ d[1] = 45 }}}
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After 1 hr, the trains are {{{ 200 - 45 = 155 }}} mi apart
Let {{{ d }}} = the distance the NY to BOS train
travels in {{{ t }}} hrs
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Equation for NY to BOS train:
(1) {{{ d = 45t }}}
Equation for BOS to NY train:
(2) {{{ 155 - d = 60t }}}
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By substitution:
(2) {{{ 155 - 45t = 60t }}}
(2) {{{ 105t = 155 }}}
(2) {{{ t = 1 + 50/105 }}}
(2) {{{ t = 1 + 10/21 }}}
{{{ ( 10/21 )*60 = 29 }}}
The trains will meet in 1 hr and 29 min
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check:
(1) {{{ d = 45t }}}
(1) {{{ d = 45*( 155/105 ) }}}
(1) {{{ d = 66.429 }}}
and
(2) {{{ 155 - d = 60t }}}
(2) {{{ 155 - d = 60*( 155/105 ) }}}
(2) {{{ 155 - d = 88.571 }}}
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{{{ 66.429 + 88.571 + 45 = 200 }}}
{{{ 155 + 45 = 200 }}}
{{{ 200 = 200 }}}
OK