Question 676175
How much of a head start does the 1st car get?
{{{ d[1] = 30*2 }}}
{{{ d[1] = 60 }}} mi
Now start a stop watch when the 2nd car leaves
Let {{{ t }}} = time on stopwatch when 2nd car catches first car
Let {{{ d }}} = distance 2nd car travels until it catches 1st car
{{{ d - 60 }}} = distance 1st car travels
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Equation for 1st car:
(1) {{{ d - 60 = 30t }}}
Equation for 2nd car:
(2) {{{ d = 42t }}}
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Substitute (2) into (1)
(1) {{{ 42t - 60 = 30t }}}
(1) {{{ 12t = 60 }}}
(1) {{{ t = 5 }}}
The 2nd car catches the 1st car in 5 hrs
check:
(2) {{{ d = 42t }}}
(2) {{{ d = 42*5 }}}
(2) {{{ d = 210 }}}
and
(1) {{{ d - 60 = 30t }}}
(1) {{{ 210 - 60 = 30t }}}
(1) {{{ 150 = 30t }}}
(1) {{{ t = 5 }}}
OK