Question

If  a car is traveling 90 miles per hour on a slippery road, then its stopping distance D in feet can be calculated by D=8100/90*1/x where x is the coefficient of friction between tires and road an 0<x<1. Multiply and simplify the formula for D. Compare the stopping distance on an icy road with x=0.2 and on dry pavement with x=0.9.

Answer 1

D=8100/90=90, so D=90/x if the equation is interpreted D=(8100/90)*1/x rather than 8100/(90*1/x). Common sense will tell us later which interpretation is right.

x=0.2: D=90/0.2=450 feet; x=0.9: D=90/0.9=100 feet. An icy road requires a longer stopping distance (450') than a dry road (100') so the correct interpretation is D=90/x. When x=0 the stopping distance is infinite because there is no friction.