The fuel efficiency rating for a certain car is 28 miles per gallon on the highway and 21 miles per gallon in the city. During one week the car traveled a total of 10.5 gallons of fuel.
a) please set up an equation(s) that would model the situation.(be sure to identify variables.)
b) how much fuel was used for highway driving? (round your answer to the nearest tenth of a gallon.)
c) how many miles where driven on the highway?( round your answer to the nearest tenth of a mile.)
a) Let's set up two equations to model the situation:
Let H be the amount of fuel used for highway driving (in gallons) and C be the amount of fuel used for city driving (in gallons).
1) H + C = 10.5 (Total amount of fuel used for the week)
2) H/28 = C/21 (Fuel efficiency in terms of gallon per mile)
b) To find out how much fuel was used for highway driving, we need to solve for H in equation (2). Let's solve the equation:
H/28 = C/21
Cross-multiplying:
21H = 28C
Dividing both sides by 28:
H = (28C)/21
We know that H + C = 10.5, so substitute the value of H:
(28C)/21 + C = 10.5
Multiply both sides by 21 to eliminate the denominator:
28C + 21C = 220.5
Combine like terms:
49C = 220.5
Divide both sides by 49:
C = 4.5
Therefore, the amount of fuel used for highway driving (H) is:
H = (28C)/21 = (28*4.5)/21 ≈ 6 gallons
c) To find out how many miles were driven on the highway, we need to multiply the fuel used for highway driving (H) by the highway fuel efficiency (28 miles per gallon):
Miles on the highway = H * 28 = 6 * 28 ≈ 168 miles
a) Let x represent the number of gallons used for highway driving and y represent the number of gallons used for city driving.
According to the fuel efficiency ratings, we can set up the following equations:
Highway Driving: x gallons at a rate of 28 miles per gallon
City Driving: y gallons at a rate of 21 miles per gallon
Since the total amount of fuel used is given as 10.5 gallons, we have:
x + y = 10.5
b) To find the amount of fuel used for highway driving, we need to solve for x. We can use the equation x + y = 10.5 and substitute y with 10.5 - x.
x + (10.5 - x) = 10.5
10.5 = 10.5
Thus, the amount of fuel used for highway driving is 10.5 gallons.
c) To find the number of miles driven on the highway, we can use the amount of fuel used for highway driving and the fuel efficiency rating of 28 miles per gallon.
Number of miles driven on the highway = fuel used for highway driving * rate of fuel efficiency
Number of miles driven on the highway = 10.5 gallons * 28 miles per gallon
Number of miles driven on the highway = 294 miles (rounded to the nearest tenth of a mile)