Answer
5 mph, 4 mph
Work Step by Step
ran 3 miles at $x$ mph and ran 4 miles at $x-1$ mph
total time was 1.6 hours
$3/x + 4/(x-1) = 1.6$
$(x)(x-1)*(3/x + 4/(x-1) = 1.6)$
$3*(x-1) + 4*x = 1.6(x)(x-1)$
$3x-3 +4x = 1.6*(x^2-x)$
$7x-3 = 1.6x^2-1.6x$
$7x-3-7x+3=1.6x^2-1.6x-7x+3$
$0 = 1.6x^2-8.6x+3$
$0=(8x-3)(.2x-1)$
$8x-3=0$
$8x=3$
$8x/8=3/8$
$x=3/8$ (not valid since we reduced our speed by 1 mph)
$.2x-1=0$
$.2x=1$
$.2*5x=1*5$
$x=5$
