Question 517969
How much of a head start in miles did Susan get?
{{{ d[1] = 45*2 }}} ( from 7 to 9 is 2 hours )
{{{ d[1] = 90 }}} mi
Start a stopwatch when Marion leaves.
Now they each will travel different distances
for the same amount of time.
Let {{{d}}} = the distance that Marion travels
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Susan's equation:
(1) {{{ d - 90 = 45t }}}
Marion's equation:
(2) {{{ d = 60t }}}
Substitute (2) into (1)
(1) {{{ 60t - 90 = 45t }}}
(1) {{{ 15t = 90 }}}
(1) {{{ t = 6 }}}
Marion will pass Susan in 6 hours
check:
(2) {{{ d = 60t }}}
(2) {{{ d = 60*6 }}}
(2) {{{ d = 360 }}}
and
(1) {{{ d - 90 = 45t }}}
(1) {{{ 360 - 90 = 45t }}}
(1) {{{ 270 = 45t }}}
(1) {{{ t = 6 }}}
OK