Let time = y and speed = x. An inverse variation equation, if time varies inversely with speed, is [tex]y= \frac{k}{x} [/tex]. We have y = 2.5 at an x of 48, so we will fill in and solve for k. [tex]2.5= \frac{k}{48} [/tex]. Multiply 2.5 times 48 to get that k = 120. Now we will use that k and a new x of 40 to find a new y, time. [tex]y= \frac{120}{40} [/tex] and y = 3. That means it will take 3 hours to travel the distance at 40 miles per hour, which of course takes longer because you're going slower.
