Question 1029152
Let {{{ s }}} = the actual speed of the biker in km/hr
Let {{{ t }}} = the time in hrs he would normally take
to arrive traveling at speed {{{ s }}}
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Equation for riving on time:
(1) {{{ 120 = s*t }}}
Equation for arriving 1 hr late:
(2) {{{ 120 = ( s-6 )*( t + 1 ) }}}
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(1) {{{ t = 120/s }}}
substitute (1) into (2)
(2) {{{ 120 = ( s-6 )*( 120/s + 1 ) }}}
(2) {{{ 120 = 120 + s - 720/s - 6 }}}
(2) {{{ 0 = s - 720/s - 6 }}}
(2) {{{ s - 6 = 720/s }}}
Multiply both sides by {{{ s }}}
(2) {{{ s^2 - 6s = 720 }}}
Complete the square
(2) {{{ s^2 - 6s + (-6/2)^2 = 720 + (-6/2)^2 }}}
(2) {{{ s^2 - 6s +9 = 720 +9 }}}
(2) {{{ ( s - 3 )^2 = 729 }}}
Take the square root of both sides
(2) {{{ s - 3 = 27 }}}
(2) {{{ s = 30 }}}
The actual speed of the biker is 30 km/hr
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check:
(1) {{{ 120 = s*t }}}
(1) {{{ 120 = 30*t }}}
(1) {{{ t = 4 }}} hrs
and
(2) {{{ 120 = ( s-6 )*( t + 1 ) }}}
(2) {{{ 120 = ( 30-6 )*( t + 1 ) }}}
(2) {{{ 120 = 24*( t + 1 ) }}}
(2) {{{ 120 = 24t + 24 }}}
(2) {{{ 24t = 96 }}}
(2) {{{ t = 4 }}} hrs
OK