Answer
jogging at 6 mph, biking at 10 mph
Work Step by Step
jogging at $x$ mph for 3 miles, biking at $x+4$ mph for 5 miles
total time is 1 hour
$3/x + 5/(x+4) = 1$
$x*(x+4)*(3/x + (5/(x+4))) = 1*x*(x+4)$
$3(x+4) + 5*x = x^4+4x$
$3x+12+5x=x^2+4x$
$8x+12 = x^2+4x$
$8x+12-8x-12 = x^2+4x-8x-12$
$0 = x^2-4x-12$
$0=(x-6)(x+2)$
$x-6=0$
$x=6$
$x+2=0$
$x=-2$ (not a valid answer since we can't have a negative speed)
$x+4$
$6+4=10$
