In preparation for a public hearing, an engineer needs to estimate the travel time savings for a proposed highway bypass of a small city in a rural area. The existing highway goes through the downtown area for 3.5 miles between the points where the bypass will connect. If the engineer anticipates a standard deviation of 5 mi/h, and would like a 95% confidence of estimating the mean speed within ±3.0 mi/h, how many runs should a travel time study include? If the engineer measures an average speed of 34.9 mi/h through the town and the bypass is expected to operate at speeds of 65 mi/h over a distance of 5.6 miles, what is the expected travel time saving per vehicle?

Question

What will be an ideal response?

Answer 1

Use Eq. 4.11 to determine the number of runs that should be conducted. Estimate N = 10 runs to begin, giving t at (1 - ?/2) and N-1 degrees of freedom = 2.262. The computed N is then 14.2, or 15. Find a new t-value with N = 15: t = 2.145, and the new computed N = 12.8, or 13.
Travel time through the town at 34.9 mi/h over 3.5 miles = 0.10 hr, or 6.0 minutes. With the anticipated bypass, it will take 5.6 mi/65 mi/h = 5.2 minutes, or a savings of 6.0 – 5.2 = 0.8 minutes per vehicle.