Chapter 3.3, Problem 34E

Traffic Flow Officials of the town of Hempstead were planning to make Hempstead Turnpike and the surrounding streets into one-way streets to prepare for the opening of Hofstra USA. In an experiment, they restricted traffic flow along the streets near Hofstra as shown in the diagram. The numbers show traffic flow per minute and the arrows indicate the direction of traffic.

a. Set up and solve the associated traffic flow problem with the following unknowns:

$x=$

Traffic per minute along the middle stretch of Oak St.

$y=$

Traffic per minute along the middle stretch of Hempstead Tpk.

$z=$

Traffic per minute along Einstein Ave.

$u=$

Traffic per minute along Party Drive.

b. If 20 cars per minute drive along Party Drive, what is the traffic like along the middle stretch of Oak Street?

c. If 20 vehicles per minute drive along Einstein Ave. and 90 vehicles per minute drive down the middle stretch of Hempstead Tpk., how many cars per minute drive along the middle stretch of Oak Street?

d. If Einstein Avenue is deserted, what is the minimum traffic along the middle stretch of Hempstead Tpk.?