Question

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​ Kindom, 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 comma 705 miles per gallon​ [mi/gal]. The Microjoule runs on ethanol. If the cars are given 100 grams​ [g] of ethanol​ (specific gravityequals0.789​) and drive until the fuel runs​ out, how far did the Microjoule drive in kilometers​ [km]?

Answer 1

Answer:

(1)  V=0.03348 gallons

(2)  L= 576.813 km .

Explanation:

Write the relation between the density and volume for ethanol.

density ( ρ )= m/V

Volume ( V )= m/ρ .......... (1)

Here, V is the volume of ethanol, m is the mass of ethanol, and  is the density of ethanol.

Write the relation between the specific gravity of ethanol and density of water

ρ=γ*ρ(water)  ............. (2)

Here,  is specific gravity of ethanol and  is the density of water.

Determine the volume of ethanol by substituting equation (2) in equation (1)

V=m/γ*ρ(water)

Substitute 100 gm , for m,  for , and 1000 kg/m  for.

V=$\frac{100*10^{-3} }{0.789*1000}$

V=0.000112674 $m^{3$

Convert m³ to gallons

V= (0.000112674*264.172 )

V=0.03348 gallons

Step 2:

Determine the distance travelled by the special vehicle named “Micro joule” runs with ethanol.

L=C*V    .......... (3)

Here,  is the rate of consumption of ethanol by Micro joule.

Substitute 10,705 mi/gallons  for C and 0.03348 gallons  for .

By using eq. 3.

L= 10750*0.03348

L=358.416 mi.

Convert the distance travelled by Micro joule from miles to kilometres

L= (358.416* 1.60934)

L = 576.813 km

Thus, the distance travelled by Micro joule is 576.813 km .