Answer
jogging: 6 mph
bike riding: 10 mph
Work Step by Step
jogging for 3 mi (x mph)
bike riding for 5 mi (x+4 mph)
$3/x + 5/(x+4) = 1$
$3*x*(x+4)/x + 5*x*(x+4)/(x+4) = 1*x*(x+4)$
$3(x+4) + 5x=x(x+4)$
$3x+12+5x=x^2+4x$
$8x+12=x^2+4x$
$x^2-4x-12=0$
$(x+2)(x-6)=0$
$x+2=0$
$x=-2$ (not a valid answer since we can't have a negative time)
$x-6=0$
$x=6$
$x+4$
$6+4$
$10$
