Question

Consider a limousine that gets m(v)= (120 - 2v) / 5 miles per gallon at speed v , whose chauffeur is paid $15/hour, and gas costs $3.5/gallon.

a. Write the function that finds the cost per mile at speed v
b. What speed results in the most inexpensive driving speed?

Answer 1

Answer:

(17.5 / 120 - 2v) + (15 / v)

Step-by-step explanation:

Given : m(v)= (120 - 2v) / 5 miles per gallon at speed v ,

chauffeur is paid $15/hour

gas cost = $3.5/gallon.

Gasoline cost per mile :

Cost per gallon = $3.5

Cost per gallon * 1/(m(v))

$3.5 * 1 / (120 - 2v) / 5

$3.5 * 5 / 120 - 2 v

= 17.5 / 120 - 2v

Time = distance / speed

Chauffeur cost = 15 per hour / v

Hence ;

Total cost :

Cost of gasoline + Cost of chauffeur

(17.5 / 120 - 2v) + (15 / v)

Answer 2

Answer would be - (17.5 / 120 - 2v) + (15 / v)

• First Given : m(v)= (120 - 2v) / 5 miles per gallon at speed v ,

• The chauffeur is paid $15/hour.

1. Then gas cost = $3.5/gallon.
2. Gasoline cost per mile :
3. Cost per gallon = $3.5
4. Cost per gallon * 1/(m(v))
5. When, $3.5 * 1 / (120 - 2v) / 5
6. $3.5 * 5 / 120 - 2 v

           Then result will be = 17.5 / 120 - 2v

        Time = distance / speed

• Chauffeur cost = 15 per hour / v

Hence ;

The total cost will be :  Cost of gasoline + Cost of chauffeur

(17.5 / 120 - 2v) + (15 / v)

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