Question 729155
Start a stop watch when the experienced cyclist leaves.
Stop it when that cyclist finishes
Let {{{ t }}} = experienced cyclist's time to finish
Let {{{ s }}} = experienced cyclists average speed
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Novice cyclist's equation:
(1) {{{ 5 - .6 = ( s - 3 )*( t + 2/60 ) }}} ( 2 min is converted to hours )
Experienced cyclist's equation:
(2) {{{ 5 = s*t }}}
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(1) {{{ 4.4 = s*t - 3t + (1/30)*s - 1/10 }}}
and
(2) {{{ s = 5/t }}}
(1) {{{ 4.4 = 5 - 3t + 1/(6t) - 1/10 }}}
(1) {{{ 26.4t = 30t - 18t^2 + 1 - (3/5)*t }}}
(1) {{{ 18t^2 - 3.6t + .6t - 1 = 0 }}}
(1) {{{ 18t^2 - 3t - 1 = 0 }}}
use quadratic formula
{{{ t = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}} 
{{{ a = 18 }}}
{{{ b = -3 }}}
{{{ c = -1 }}}
{{{ t = (-(-3) +- sqrt( (-3)^2 - 4*18*(-1) ))/(2*18) }}} 
{{{ t = ( 3 +- sqrt( 9 + 72 ))/ 36 }}} 
{{{ t = ( 3 +- sqrt( 81 ))/ 36 }}} 
{{{ t = ( 3 + 9 ) / 36 }}}
{{{ t = 12/36 }}}
{{{ t = 1/3 }}}
and
(2) {{{ 5 = s*t }}}
(2) {{{ s = 5/(1/3) }}}
(2) {{{ s = 15 }}}
{{{ s - 3 = 12 }}}
The novice's speed is 12 mi/hr
check:
(1) {{{ 5 - .6 = ( s - 3 )*( t + 2/60 ) }}}
(1) {{{ 5 - .6 = ( 15 - 3 )*( 1/3 + 1/30 ) }}}
(1) {{{ 4.4 = 12*( 11/30 ) }}}
(1) {{{ 4.4 = 132/30 }}}
(1) {{{ 132 = 132 }}}
OK