Answer
a) 11.615 m/s
b) 11.612 m/s
c) 25.975 mph
Work Step by Step
b)
Distance = rate * time
For Contador, we use the following variables
rate (in meters/second) = $x$
time (in seconds) = $y$
Total distance = 119 kilometers (119,000 meters)
Contador: $119000 =x*y$
Voeckler was .0034 meters/second faster and took 3 seconds fewer
Voeckler: $119000 = (x+.0034)*(y-3)$
$119000 = (x+.0034)*(y-3)$
$119000 = x*y+x*-3+.0034*y+.0034*-3$
$119000 = xy-3x+.0034y-.0102$
$119000 =x*y$
$119000 = xy-3x+.0034y-.0102$
$xy=xy-3x+.0034y-.0102$
$xy-xy=xy-3x+.0034y-.0102-xy$
$0=-3x+.0034y-.0102$
$0+3x=-3x+.0034y-.0102+3x$
$3x=.0034y-.0102$
$3x/3=(.0034y-.0102)/3$
$x=.001133333y-.0034$
$119000 =x*y$
$119000 =(.001133333y-.0034)*y$
$119000 =.001133333y^2-.0034y$
$119000-119000 =.001133333y^2-.0034y-119000$
$0 =.001133333y^2-.0034y-119000$
$a=.0011333333$, $b=-.0034$, $c=-119000$
$y=(-b±\sqrt{b^2-4ac})/2a$
$y=(.0034±\sqrt{(-.0034)^2-4*.00113333*-119000})/2*.00113333$
$y=(.0034±\sqrt{(-.0034)^2+4*.113333*1190})/.00226666$
$y=(.0034±\sqrt{.00001156+539.46508})/.00226666$
$y=(.0034±\sqrt{539.46509156})/.00226666$
$y=(.0034±23.22638)/.00226666$
We want only the positive square root as we are looking for time.
$y=(.0034+23.22638)/.00226666$
$y=23.22978/.00226666$
$y=10248.432$
$119000/10248.432 =11.6115$ m/s
Rounded to three decimal places, $x=11.612$ m/s.
a)
Vocekler was .0034 m/s faster, so $11.6115+.0034=11.6149$
Rounded to three decimal places, Vocekler's speed was $11.615$ m/s
c)
$11.615$ meters/second $* 3.28084$ feet/meter $*3600$ seconds/hour = $137149.92$ feet/hour
$137149.92$ feet/hour $*1/5280$ miles/feet = $25.975$ mi/hr
