Question 876747
How much of a head start does the bus have?
{{{ d[1] = 28*( .25 ) }}}
{{{ d[1] = 7 }}} mi
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Start a stopwatch when her mom leaves
Let {{{ t }}} = time on stopwatch when she
catches up with the bus
Let {{{ d }}} = the distance that her mom
travels until she catches bus
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The buses equation:
(1) {{{ d - 7 = 28t }}}
Mom's equation:
(2) {{{ d = 42t }}}
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(1) {{{ d = 28t + 7 }}}
By substitution:
{{{ 28t + 7 = 42t }}}
{{{ 14t = 7 }}}
{{{ t = 1/2 }}} hr
Emily's mom will catch the bus in 30 min
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check:
(1) {{{ d - 7 = 28*( 1/2 ) }}}
(1) {{{ d = 21 }}}
and
(2) {{{ d = 42*( 1/2 ) }}}
(2) {{{ d = 21 }}}
OK