A study showed that during the peak-hour commute on two routes connecting a suburb with a large city, there are a total of 5500 vehicles that make the trip. Route 1 is 7 miles long with a 65-mi/h speed limit and route 2 is 4 miles long with a speed limit of 50 mi/h. The study also found that the travel time on route 2 increases with the square of the number of vehicles, while the route 1 travel time increases two minutes for every 500 additional vehicles added. Determine the user-equilibrium travel time in minutes.

A study showed that during the peak-hour commute on two routes connecting a suburb with a large city, there are a total of 5500 vehicles that make the trip. Route 1 is 7 miles long with a 65-mi/h speed limit and route 2 is 4 miles long with a speed limit of 50 mi/h. The study also found that the travel time on route 2 increases with the square of the number of vehicles, while the route 1 travel time increases two minutes for every 500 additional vehicles added. Determine the user-equilibrium travel time in minutes.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A study showed that during the peak-hour commute on two routes
connecting a suburb with a large city, there are a total of 5500 vehicles that
make the trip. Route 1 is 7 miles long with a 65-mi/h speed limit and route 2 is
4 miles long with a speed limit of 50 mi/h. The study also found that the travel
time on route 2 increases with the square of the number of vehicles, while
the route 1 travel time increases two minutes for every 500 additional
vehicles added. Determine the user-equilibrium travel time in minutes. *

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