Answer
$2500/(r+100) + 2500/r$
$(5000r + 250000)/r(r+100)$
Work Step by Step
LA to NY: rate = $r+100$
NY to LA: rate = $r$
$(r+100)*t = 2500$
$t = 2500/(r+100)$
$r*t = 2500$
$t = 2500/r$
$2500/(r+100) + 2500/r$
$2500/(r+100)*r/r + 2500/r*(r+100)/(r+100)$
$2500r/r(r+100) + 2500(r+100)/r*(r+100)$
$2500r + 2500r + 250000 / r(r+100)$
$5000r + 250000/r(r+100)$