Question 768994
What is the 1st car's head start?
{{{ d[1] = 10*10 = 100 }}} mi
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Start a stopwatch when the 2nd car leaves
Let {{{ t }}} = the time on the stopwatch in
hours when they meet
Let {{{ d }}} = rhe distance in miles that the
2nd car travels in time {{{ t }}}
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1st car's equation:
(1) {{{ d - 100 = 10t }}}
2nd car's equation:
(2) {{{ d = 60t }}}
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By substitution:
(1) {{{ 60t - 100 = 10t }}}
(1) {{{ 50t = 100 }}}
(1) {{{ t = 2 }}}
and
(2) {{{ d = 60*2 }}}
(2) {{{ d = 120 }}}
The cars meet 120 miles from the starting point
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check:
(1) {{{ d - 100 = 10t }}}
(1) {{{ d - 100 = 10*2 }}}
(1) {{{ d = 120 }}}
OK