The merged lane will need to have twice as many cars passing a given point in a given time period than the initial pair of lanes, or conversely will take half the time for each car to pass a given point.

Say the initial speed is x (mph), then the stopping distance is (x^2)/20 + x/2 (ft).

If we take this distance and divide by the speed x we will know the time taken for each car to pass a given point. (The units for this are 15/22 seconds, but we don’t need to worry about that since it’s the same whatever the speed).

The formula for this measure is x/20 + 1/2.

To merge the lanes we need to find a value y such that y/20 + 1/2 is half as much as x/20 + 1/2:

y/10 + 1 = x/20 + 1/2

y/10 = x/20 – 1/2

y = x/2 – 5

For our puzzle x=60, and so therefore y = 25mph.