Question 770404
Let {{{ d }}} = the distance to work in miles
Let {{{ s }}} = his speed in mi/hr on Monday
{{{ s + 9 }}} = his speed on Tuesday
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Equation for Moday:
(1) {{{ d = s*( 35/60 ) }}} ( the time is converted to hours )
Equation for Tuesday:
(2) {{{ d = ( s + 9 )*( ( 35 - 7 ) / 60 ) }}}
(2) {{{ d = ( s + 9 )*( 28/60 ) }}}
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(2) {{{ d = ( s + 9 )*( 7/15 ) }}}
(2) {{{ 15d = 7s + 63 }}}
(2) {{{ 15d - 7s = 63 }}}
and
(1) {{{ d = s*( 7/12 ) }}}
(1) {{{ 12d = 7s }}}
(1) {{{ 12d - 7s = 0 }}}
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Subtract (1) from (2)
(2) {{{ 15d - 7s = 63 }}}
(1) {{{ -12d + 7s = 0 }}}
{{{ 3d = 63 }}}
{{{ d = 21 }}}
The distance to work and back is 42 mi
check:
(1) {{{ d = s*( 7/12 ) }}}
(1) {{{ 21 = s*( 7/12 ) }}}
(1) {{{ 7s = 252 }}}
(1) {{{ s = 36 }}}
and
(2) {{{ 15d - 7s = 63 }}}
(2) {{{ 15*21 - 7s = 63 }}}
(2) {{{ 315 - 7s = 63 }}}
(2) {{{ 7s = 315 - 63 }}}
(2) {{{ 7s = 252 }}}
(2) {{{ s = 36 }}}
OK