Question 649492
Let {{{ d }}} = the distance in km between house and office
Let {{{ t }}} = The travel time in hrs which is on time for him
given:
From office to house at 5 km/hr
(1) {{{ d = 5*( t + 10/60 ) }}}
From office to house at 6 km/hr
(2) {{{ d = 6*( t - 10/60 ) }}}
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(1) {{{ d = 5t + 5/6 }}}
(2) {{{ d = 6t - 1 }}}
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Substitute (1) into (2)
(2) {{{ 5t + 5/6 = 6t - 1 }}}
(2) {{{ t = 5/6 + 1 }}}
(2) {{{ t = 11/6 }}}
Plug this result back into (1) or (2)
(1) {{{ d = 5*(11/6) + 5/6 }}}
(1) {{{ d = 55/6 + 5/6 }}}
(1) {{{ d = 10 }}}
 the distance between his house and office is 10 km
check:
(2) {{{ d = 6t - 1 }}}
(2) {{{ 10 = 6t - 1 }}}
(2) {{{ 6t = 11 }}}
(2) {{{ t = 11/6 }}}
OK
(1) {{{ d = 5t + 5/6 }}}
(1) {{{ 10 = 5t + 5/6 }}}
(1) {{{ 5t = 10 - 5/6 }}}
(1) {{{ 5t = 60/6 - 5/6 }}}
(1) {{{ 5t = 55/6 }}}
(1) {{{ t = 11/6 }}}
OK