Question 701652
Let {{{ t }}} = the time in seconds for the faster runner
{{{ 29 - t }}} = the time in seconds for the slower runner
Let {{{ s }}} = the speed of the slower runner in m/sec
{{{ s + .55 }}} = the speed of the faster runner in m/sec
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For slower runner:
(1) {{{ 100 = s*( 29 - t ) }}}
For the faster runner:
(2) {{{ 100 = ( s + .55 )*t }}}
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(1) {{{ 100 = 29s - s*t }}}
and
(2) {{{ t = 100 / ( s + .55 ) }}}
Substitute (2) into (1)
(1) {{{ 100 = 29s - s*( 100 / ( s + .55 )) }}}
(1) {{{ 100*( s + .55 ) = 29s*( s + .55 ) - 100s }}}
(1) {{{ 100s + 55  = 29s^2 + 15.95s - 100s }}}
(1) {{{ 29s^2  = 55 - 15.95s }}}
(1) {{{ 29s^2 + 15.95s - 55 = 0 }}}
use quadratic formula
{{{ s = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 29 }}}
{{{ b = 15.95 }}}
{{{ c = -55 }}}
{{{ s = ( -15.95 +- sqrt( 15.95^2 - 4*29*(-55) )) / (2*29) }}}
{{{ s = ( -15.95 +- sqrt( 254.4025 + 6380 )) / 58 }}}
{{{ s = ( -15.95 +- sqrt( 6634.4 )) / 58 }}}
{{{ s = ( -15.95 + 81.452 ) / 58 }}}
{{{ s = 65.5 / 58 }}}
{{{ s = 1.1293 }}}
{{{ s + .55 = 1.6793 }}}
The slower runner's speed is 1.1293 m/sec
The faster runners speed is 1.6793 m/sec
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check:
(1) {{{ 100 = 1.1293*( 29 - t ) }}}
(1) {{{ 100 = 32.7497 - 1.1293t }}}
(1) {{{ 1.1293t = 67.2503 }}}
(1) {{{ t = 59.5504 }}}
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(2) {{{ 100 = ( 1.1293 + .55 )*t }}}
(2) {{{ 100 = 1.6793*t }}}
(2) {{{ t = 59.549 }}}
close enough
hope I got it