## Problem of the Day #19: Race of ComplexityApril 7, 2011

Posted by Aziz in : potd , trackback

Several capitalists have developed a sickly condition known as capital overflow. To cure themselves, they decide to construct a race track in the shape of a regular pentagon and race against each other.

In order to cure their sickness, they purchase SUVs with the worst possible mileage: $5$mpg in city, and $10$mpg on highway. Furthermore, the SUVs can only hold up to $3$ gallons of fuel at any given time.

The vertices of the race track serve are mini cities. In relation to the race track, they are simply points, but the SUVs have to drive $3$ miles to get through them. The edges of the race track are $15$ miles long.

While in a city, an SUV can refuel up to 1.5 gallons of fuel. The amount of time in minutes that it takes to refuel is double the amount of fuel in gallons that is refueled.

The original goal was to maximize everything, but recent regulations have forced the giddy capitalists into severe restrictions:

1. A race must consist of one lap around the track.
2. They must minimize the time it takes for them to complete a race.
3. They must minimize the amount of fuel they use for the race.
5. They must begin at one of the vertices with a full tank.
4. They MUST finish the race.

Determine the minimum amount of fuel needed for an SUV to complete a race. Determine the minimum possible time it takes for an SUV to finish a race.

BONUS:
Determine the minimum sum of the amount of fuel in gallons and time in minutes that an SUV can attain in a single race.

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