Answer
50 mph to the beach, 60 mph from the beach
Work Step by Step
To Beach: $x$ hrs, $y$ mph
From Beach: $55/3-x$ hrs, $y+10$ mph
$\frac{500}{y} + \frac{500}{(y+10)} = \frac{55}{3}$
$3*y*(y+10)*\frac{500}{y} + 3*y*(y+10)*\frac{500}{(y+10)} = 3*y*(y+10)*\frac{55}{3}$
$3*(y+10)*500+3y*(500)=y*(y+10)*55$
$1500*(y+10)+1500y=55y*(y+10)$
$1500y+15000+1500y=55y^2+550$
$3000y+15000=55y^2+550y$
$0=55y^2-2450y-15000$
$y=(-b±\sqrt{b^2-4ac})/2a$
$y=(-(-2450)±\sqrt{(-2450)^2-4*55*(-15000)})/2*55$
$y=(2450±\sqrt{6002500+220*(15000)})/110$
$y=(2450±\sqrt{6002500+3300000})/110$
$y=(2450±\sqrt{9302500})/110$
$y=(2450±3050)/110$
Since we would have a negative value for $y$ if we use the negative square root, we will not use the negative square root.
$y=(2450±3050)/110$
$y=(2450+3050)/110$
$y=5500/110$
$y=50$
$y+10$
$50+10$
$60$
