A car goes 18 miles on a gallon of gas in city driving and 24 miles on the highway. If the car goes 465 miles on a full tank of 23 gallons of gas, how many miles were driven in the city and how many miles were driven on the highway?
miles on the highway --- x
miles in the city ----- 465-x
gallons used on highway = x/24
gallons used in city = (465-x)/18
x/24 + (465-x)/18 = 23
multiply each term by 72 , the LCD
3x + 4(465-x) = 1656
3x + 1860 - 4x = 1656
-x=-204
x = 204
Miles on the highway were 204
check:
highway: 204, number of gallons = 8.5
city: 261, number of gallons = 14.5
8.5 +14.5 = 23
To solve this problem, we can use a system of equations. Let's assume the car drove x miles in the city and y miles on the highway.
From the given information, we can set up two equations:
Equation 1: x/18 + y/24 = 465/23 (since the total distance driven is equal to 465 miles and the total gas used is 23 gallons)
Equation 2: x + y = 465 (since the total distance driven is equal to 465 miles)
Now, let's solve this system of equations to find the values of x (miles driven in the city) and y (miles driven on the highway):
First, let's simplify Equation 1 by multiplying all terms by the common denominator of 72:
4x + 3y = 960
Next, let's solve the system of equations using the method of substitution or elimination. I'll use the elimination method here:
Multiply Equation 2 by 3 to make the coefficients of y in both equations equal:
3x + 3y = 1395
Now, subtract this modified equation from Equation 1:
(4x + 3y) - (3x + 3y) = 960 - 1395
x = -435
We have found that x = -435, which means the car traveled -435 miles in the city. This doesn't make sense in this context since distance cannot be negative. Therefore, there must be an error in the problem or the data provided.
Please check the given information and make sure all values are accurate.