Frank's car can travel 30 miles per gallon of gas. Janet's car can travel 20 miles per gallon of gas. Frank and Janet drive their own cars and they leave for a trip at 8.00AM on Friday. They arrive at their destination at 2.00AM the next day. Saturday, after driving at an average speed of 40 miles per hour for the trip. The total amount of money spent on gas for the two cars together was $ 165.00 How much did each gallon of gas cost?
Their trip takes 30 hours. If they average 40 mph, the trip length is 1200 miles.
Let X be the cost of a gallon of gas.
165.00 = [(1200/30) + (1200/20)]*X
= (40 + 60 gallons)* X ($/gallon)
Solve for X
To find out how much each gallon of gas cost, we need to solve the problem by breaking it down into smaller steps. Here's how we can approach it:
Step 1: Determine the distance traveled
Since Frank and Janet drive from 8.00AM on Friday until 2.00AM the next day, they drive for a total of 18 hours (8.00AM - 2.00AM).
To find the distance traveled, we multiply the average speed of 40 miles per hour by the total time of 18 hours:
Distance traveled = Speed × Time
Distance traveled = 40 miles/hour × 18 hours = 720 miles
Step 2: Calculate the gas consumption for each car
Frank's car travels 30 miles per gallon, so the number of gallons Frank's car uses is:
Gallons used by Frank = Distance traveled / Miles per gallon = 720 miles / 30 miles/gallon = 24 gallons
Similarly, Janet's car travels 20 miles per gallon, so the number of gallons Janet's car uses is:
Gallons used by Janet = Distance traveled / Miles per gallon = 720 miles / 20 miles/gallon = 36 gallons
Step 3: Calculate the cost per gallon
Let's assume the cost per gallon of gas is "x" dollars.
The cost of gas for Frank's car is 24 gallons × x dollars/gallon = 24x dollars.
The cost of gas for Janet's car is 36 gallons × x dollars/gallon = 36x dollars.
The total amount spent on gas for both cars is $165. So we have the equation:
Total gas cost = Frank's gas cost + Janet's gas cost
$165 = 24x + 36x
Step 4: Solve the equation for x
Combine like terms:
$165 = 60x
Divide both sides by 60:
$2.75 = x
So, each gallon of gas costs $2.75.
Therefore, each gallon of gas costs $2.75.