Problem Solving

A hybrid car has a 15-gallon fuel tank and uses one gallon of fuel to travel 45 miles. If the driver of the car begins her trip with a full tank and drives for 8 hours at a constant rate of 60 miles per hour, what fraction of her fuel tank is full at the end of the trip?

A. \(\dfrac29\)

B. \(\dfrac{11}{48}\)

C. \(\dfrac{13}{45}\)

D. \(\dfrac13\)

E. \(\dfrac{17}{48}\)

Answer: C

Source: Veritas Prep

VJesus12 wrote: ↑

Wed Nov 17, 2021 1:01 pm

A hybrid car has a 15-gallon fuel tank and uses one gallon of fuel to travel 45 miles. If the driver of the car begins her trip with a full tank and drives for 8 hours at a constant rate of 60 miles per hour, what fraction of her fuel tank is full at the end of the trip?

A. \(\dfrac29\)

B. \(\dfrac{11}{48}\)

C. \(\dfrac{13}{45}\)

D. \(\dfrac13\)

E. \(\dfrac{17}{48}\)

Answer: C

Source: Veritas Prep

Fuel tank capacity \(= 15\) G
Car burns \(1\) G for each \(45\) miles driven
After driving for \(8\) hours at \(60\) miles/hour \(\Longrightarrow\) Distance driven \(= 8*60 = 480\) miles
Gas burnt to drive \(480\) miles \(= \dfrac{480}{45}\) G

Gas left in the tank \(= 15 - \dfrac{480}{45} = 15 - \dfrac{32}{3} = \dfrac{13}{3}\) G

Fraction of gas left to total capacity \(= \dfrac{\,\dfrac{13}{3}\,}{15} = \dfrac{13}{45}\)