Chapter 6 - Section 6.7 - Quadratic Equations and Problem Solving - Exercise Set - Page 468: 50

8 mph and 15 mph

$x^2+(x+7)^2=17^2$ $x^2+x^2+14x+49=289$ $2x^2+14x-240=0$ $(2x^2+14x-240=0)/2$ $x^2+7x-120=0$ $x^2+15x-8x-120=0$ $x(x+15)-8(x+15)=0$ $(x+15)(x-8)=0$ $x+15=0$ $x=-15$ (invalid since we can't have negative speeds) $x-8=0$ $x=8$ $8+7=15$