The Eco-Marathon is an annual competition sponsored by Shell Oil, in which participants build special vehicles to achieve the highest possible fuel efficiency. The Eco-Marathon is held around the world with events in the United Kingdom, Finland, France, Holland, Japan, and the United States. A world record was set in Eco-Marathon by a French team in 2003 called Microjoule with a performance of 10,705 miles per gallon. The Microjoule runs on ethanol. If the cars are given 100 grams of ethanol (specific gravity = 0.789) and drive until the fuel runs out, how far did the Microjoule drive in kilometers?

Mileage of vehicle = 10705 miles per gallon

mass of fuel, m = 100 gms of ethanol

= (100 / 1000) kg

= 0.1 kg of ethanol

specific gravity = 0.789

density of fuel, d = specific gravity X density of water

= 0.789 X 1000 kg / m3

= 789 kg / m3

Volume of fuel stored in the vehicle in m3 = m / d

= 0.1 / 789

= 1.267 X 10-4 m3

Since 1 m3 = 264.172 gallons

Hence volume of fuel in gallons = volume of fuel in m3 X 264.172

= 1.267 X 10-4 X 264.172

= 0.0335 gallons

Distance covered by the vehicle in miles, = Mileage of vehicle X volume of fuel in gallons

= 10705 X 0.0335

= 358.42 miles

Since 1 mile = 1.609 km

Hence distance covered by the vehicle in kilometres = (distance convered by vehicle in miles) X 1.609

= 358.42 X 1.609

= 567.7 km