Afamily takes 2 1/2 hours to drive from their house to a lake at 48 mi/h. the travel time varies inversely with the speed of the car. how long will the return trip take at 40 mi/h?

Let time = y and speed = x.  An inverse variation equation, if time varies inversely with speed, is .  We have y = 2.5 at an x of 48, so we will fill in and solve for k.  .  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.  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.