Answer
5 mph for 3 miles, 4 mph for 4 miles
Work Step by Step
Speed at 3 miles: x mph
Speed at 4 miles: (x-1) mph
$3/x + 4/(x-1) = 8/5$
$3*x/x + 4*x/(x-1) = 8*x/5$
$3*5 + 4*x*5/(x-1) = 8*x*5/5$
$15 + 20x/(x-1) = 8x$
$15*(x-1) + 20x*(x-1)/(x-1) = 8x*(x-1)$
$15*(x-1) + 20x = 8x*(x-1)$
$15x-15+20x=8x^2-8x$
$35x-15=8x^2-8x$
$8x^2-43x+15=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-43)±\sqrt {(-43)^2-4*8*15})/2*8$
$x=(43±\sqrt {(-43)^2-60*8})/16$
$x=(43±\sqrt {1849-480})/16$
$x=(43±\sqrt {1369})/16$
$x=(43±37)/16$
$x=(43±37)/16$
$x=(43+37)/16$
$x=80/16$
$x=5$
$x=(43±37)/16$
$x=(43-37)/16$
$x=6/16$
$x=3/8$
A speed of 3/8 mph would provide a negative denominator for the second fraction. Thus, we would have a negative speed.
$x-1$
$5-1$
$4$
