Question

Gas mileage actually varies slightly with the driving speed of a car​ (as well as with highway vs. city​ driving). Suppose your car averages 33 miles per gallon on the highway if your average speed is 48 miles per​ hour, and it averages 29 miles per gallon on the highway if your average speed is 67 miles per hour.
a. What is the driving time for a 2600​-mile trip if you drive at an average speed of 48 miles per​ hour? What is the driving time at 67 miles per​ hour?

The driving time at 48 miles per hour is ___ hours.
​(Type an integer or decimal rounded to two decimal places as​ needed.)

The driving time is at 67 miles per hour is __hours.
​(Round to two decimal places as​ needed.)

b. Assume a gasoline price of ​$3.05 per gallon. What is the gasoline cost for a 2600​-mile trip if you drive at an average speed of 48 miles per​ hour?
What is the gasoline cost at 67 miles per​ hour?

The gasoline cost at 48 miles per hour is ​$:
​(Round to two decimal places as​ needed.)

The gasoline cost at 67 miles per hour is $​:
​(Round to two decimal places as​ needed.)

Answer 1

Answer:

a)

First part: "The driving time at 48 miles per hour is 54.17 hours."

Second part: "The driving time at 67 miles per hour is 38.81 hours."

b)

First part:  "The gasoline cost at 48 miles per hour is ​$240.30"

Second part:

"The gasoline cost at 67 miles per hour is $​273.45"

Step-by-step explanation:

a)

We use the equation  $D=RT$  to solve this. Where D is the distance, R is the rate (speed), and T is the time.

First part:

The distance is 2600 miles (D) and the rate (R) is 48 mph, so time is:

$D=RT\\2600=(48)T\\T=\frac{2600}{48}\\T=54.17$

"The driving time at 48 miles per hour is 54.17 hours."

Second part:

The distance is 2600 miles (D) and the rate (R) is 67 mph, so time is:

$D=RT\\2600=(67)T\\T=\frac{2600}{67}\\T=38.81$

"The driving time at 67 miles per hour is 38.81 hours."

b)

First part:

At 48mph, the fuel consumption is 33 miles per gallon. The number of gallons needed is 2600 divided by 33:

Number of Gallons = $\frac{2600}{33}=78.79$

Total cost @ 3.05 per gallon = 78.79*3.05=$240.30

"The gasoline cost at 48 miles per hour is ​$240.30"

Second part:

At 67 mph, the fuel consumption is 29 miles per gallon. The number of gallons needed is 2600 divided by 29:

Number of Gallons = $\frac{2600}{29}=89.66$

Total cost @ 3.05 per gallon = 89.66*3.05=$273.45

"The gasoline cost at 67 miles per hour is $​273.45"