physics
posted by andy on .
Along a straight road through town, there are three speedlimit signs. They occur in the following order: 56 , 33 , and 24 mi/h, with the 33 mi/h sign located midway between the other two. Obeying these speed limits, the smallest possible time tA that a driver can spend on this part of the road is to travel between the first and second signs at 56 mi/h and between the second and third signs at 33 mi/h. More realistically, a driver could slow down from 56 to 33 mi/h with a constant deceleration and then do the same thing from 33 to 24 mi/h. This alternative requires a time tB. Find the ratio tB/tA

Let L be the distance between signs. It is the same for the 56 and the 33 mph segments.
tA = L/56 + L/33 = L/20.764
tB = L/44.5 + L/28.5 = L/17.373
44.5 and 28.5 are the average speeds in the two segments, while decelerating.
tB/tA = 1.195