Answer
25.925 mph
Work Step by Step
Voeckler was .0034 m/s faster than Contador
Contador took 3 seconds more than Voeckler
Voeckler: $119*1000 = (x+.0034)*t$
Contador: $119*1000 = x*(t+3)$
$119000 = xt + .0034t$
$119000 = xt + 3x$
$xt + .0034t = xt +3x$
$.0034t = 3x$
$.0034t/3 = 3x/3$
$.0011333333t = x$
$119000 = (x+.0034)*t$
$119000 = (.0011333333t+.0034)*t$
$119000 = (.0011333333t^2+.0034t)$
$119000-(.0011333333t^2+.0034t)=.0011333333t^2+.0034t-(.0011333333t^2+.0034t)$
$119000-.0011333333t^2+.0034t=0$
$-.0011333333t^2+.0034t+119000=0$
A graphing calculator showed $t= -10245.451$ and $t=10248.451$. However, we ignore the first value of $t$ since we can't have negative time.
$t=10248.451$
This is the same as 2.846 hours
Voeckler: $119*1000 = (x+.0034)*t$
$119000 = (x+.0034)*10248.451$
$119000/10248.451 = (x+.0034)*10248.451/10248.451$
$11.6115 = x+.0034$
$11.6115 - .0034 = x+.0034-.0034$
$11.6081 = x$
We needed Voeckler's speed--$11.6115+.0034$
$11.6115+.0034$
$11.6149$ meters/second
meters/ second *1/ 1000 = km/second
km/second 60 = km/minute
km/minute *60 = km/hr
km/hr * .62 = miles/hr
meters/second * 1/1000*60*60*.62 = miles/hr
m/s * 2.232 = mi/hr
11.6149 m/s * 2.232= 25.92445 mph
