Question 955829
In {{{ 1.25 }}} hrs, the 1st ship travels:
{{{ d[1] = 40*1.25 }}}
{{{ d[1] = 50 }}} mi
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Start a stopwatch when 2nd ship leaves
Let {{{ t }}} = time in hrs when 2nd ship
catches the 1st ship
Let {{{ d }}} = distance from port A when
2nd ship catches 1st ship
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Equation for 1st ship:
(1) {{{ d - 50 = 40t }}}
Equation for 2nd ship:
(2) {{{ d = 60t }}}
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Substitute (2) into (1)
(1) {{{ 60t - 50 = 40t }}}
(1) {{{ 20t = 50 }}}
(1) {{{ t = 2.5 }}}
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and
(2) {{{ d = 60*2.5 }}}
(2) {{{ d = 150 }}}
150 mi from port A, 2nd ship catches the 1st ship
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check:
(1) {{{ d - 50 = 40t }}}
(1) {{{ 150 - 50 = 40*2.5 }}}
(1) {{{ 100 = 100 }}}
OK