Question 883180
Ma has to drive faster, or else she
can't catch Pa
Pa's speed  = {{{ 30 }}} mi/hr
Let Ma's speed = {{{ 30 + s }}} mi/hr
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How much of a head start does Pa get?
{{{ d[1] = 30*1 }}}
{{{ d[1] = 30 }}} mi
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Start a stop watch when Ma leaves
Let {{{ d }}} = the distance Ma has traveled
when she catches Pa
Let {{{ s }}} = Ma's speed in mi/hr
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Pa's equation:
(1) {{{ d - 30 + 10 = 30*4 }}}
Ma's equation:
(2) {{{ d + 10 = s*4 }}}
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(1) {{{ d - 20 = 120 }}}
(1) {{{ d = 140 }}}
Substitute this value into (2)
(2) {{{ 140 + 10 = 4s }}}
(2) {{{ 4s = 150 }}}
(2) {{{ s = 37.5 }}}
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Ma is driving 37.5 mi/hr
check:
(2) {{{ d + 10 = s*4 }}}
(2) {{{ 140 + 10 = 37.5*4 }}}
(2) {{{ 150 = 150 }}}
OK