Difference in the total number of person-minutes

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Every morning, 2,000 commuters must travel from North Nanaimo to South Nanaimo. Commuters all try to minimize the time it takes to get to work. There are two ways to make the trip. One way is to drive straight across town, throught the heart of Nanaimo. The other way is to take the 19 Highway that circles Nanaimo. The Highway is entirely uncongested, but the drive is roundabout and it takes 20 minutes to get from North to South by this means. The road through Nanaimo is much shorter, and if it were uncongested, it would take only 10 minutes to travel from North to South by this means. But this road can get congested. In fact, if the number of commuters who use this road is N, then the number of minutes that it takes to drive from North to South through Nanaimo is 10 + N=50

(a) Assuming that no tolls are charged for using either road, how many commuters will use the road through Nanaimo?

(b) Suppose that commuters value time saved from commuting at $2 per minute and that the Greater Nanaimo Mayor charges a toll for using the road through Nanaimo (shorter one) and divides the revenue from this toll equally among all 2,000 commuters. If the mayor chooses a toll of $15 for the short route, how many commuters would take the shorter route?

(c) What is the difference in the total number of person-minutes spent in cars before and after the toll?

Reference no: EM132730125

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