Question 1038787
Let {{{ d }}} = distance from home to school
Let {{{ t }}} = time in hrs B takes at 6 km/hr
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(a)
(1) {{{ d = 6t }}}
(2) {{{ d = 8*( 70/60 - t ) }}}
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(2) {{{ d = 560/60 - 8t }}}
Substitute (1) into (2)
(2) {{{ 6t = 56/6 - 8t }}}
(2) {{{ 14t = 28/3 }}}
(2) {{{ t = 2/3 }}} 
and
(1) {{{ d = 6t }}}
(1) {{{ d = 6*(2/3) }}}
(1) {{{ d = 4 }}}
The distance from home to school is 4 km
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(b)
(1) {{{ d = 30t }}}
(2) {{{ d = 50*( 5 - t ) }}}
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(2) {{{ d = 250 - 50t }}}
Substitute (1) into (2)
(2) {{{ 30t = 250 - 50t }}}
(2) {{{ 80t = 250 }}}
(2) {{{ t = 25/8 }}}
and
(1) {{{ d = 30t }}}
(1) {{{ d = 30*(25/8) }}}
(1) {{{ d = 15*( 25/4 ) }}}
(1) {{{ d = 93.75 }}} 
{{{ 2d = 187.5 }}}
the total distance is 187.5 km
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check:
(1) {{{ d = 30t }}}
(1) {{{ 93.75 = 30*(25/8) }}}
(1) {{{ 750 = 30*25 }}}
(1) {{{ 750 = 750 }}}
and
(2) {{{ d = 50*( 5 - t ) }}}
(2) {{{ 93.75 = 50*( 5 - 25/8 ) }}}
(2) {{{ 93.75 = 250 - 50*( 25/8 ) }}}
(2) {{{ 750 = 8*250 - 25*50 }}}
(2) {{{ 750 = 2000 - 1250 }}}
(2) {{{ 750 = 750 }}}
OK