If you rent a car, you can (1) return it with a full gas tank, (2) return it without filling it and pay $3.45/gallon or (3) accept a fixed price of $35 for full tank of gas. The local price is $3.15/gallon of gasoline and you expect the car to get 28 mpg. The car has 20-gallon tank. What choice should you make if you expect to drive?

a) 150 miles

b) 350 miles

c) 500 miles

d) How do your answers change if stopping at filling station takes 15 minutes and your time is worth $12/hr

Question

11-02-2020
Mathematics

contestada

If you rent a car, you can (1) return it with a full gas tank, (2) return it without filling it and pay $3.45/gallon or (3) accept a fixed price of $35 for full tank of gas. The local price is $3.15/gallon of gasoline and you expect the car to get 28 mpg. The car has 20-gallon tank. What choice should you make if you expect to drive?

a) 150 miles

b) 350 miles

c) 500 miles

d) How do your answers change if stopping at filling station takes 15 minutes and your time is worth $12/hr

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lucianoangelini92 lucianoangelini92 · Answer 1 · 2020-02-12T13:35:12+01:00

Answer:

a) return it with a full gas tank

b) return it with a full gas tank

c) accept a fixed price

d) answers do not change

Step-by-step explanation:

considering the 3 scenarios under the assumption that the car initially has the tank full , then:

1) return it with a full gas tank : cost=$3.15 /gallon / (28 miles/gallon)* number of miles

2) return it without filling it: cost= $3.45 /gallon / (28 miles/gallon) * number of miles

3) accept a fixed price: $35

then option 1 is always better than option 2. The option 1 is better than the third when

$3.15 /gallon / (28 miles/gallon)* number of miles < $35

number of miles < 35/3.15*28 = 311 miles

then the choice for

a) return it with a full gas tank

b) return it with a full gas tank

c) accept a fixed price

for d) , assuming the best case scenario that the filling station is on the main pathway so you do not have to deviate to reach the station, then the cost for option 1 is altered

1) return it with a full gas tank : cost= cost of filling the tank + cost for the stops at the filling station

cost=$3.15 /gallon / (28 miles/gallon)* number of miles + $12/(hour*stop) * 15 min* 1 hour/60 min * 1 stop/20 gallons / (28 miles/gallon) * number of miles = $ 0.1178 /mile * number of miles

while option 2) remains the same : $0.1232/mile*number of miles

then option 1 is still better than option 2. The option 1 is better than the third when

$ 0.1178 /mile*number of miles < $35

number of miles < 35/0.1178 = 297 miles

then the answers do not change