The Honda Civic Hybrid vehicle, powered by gasoline-electric technology, gets 49 miles per gallon in city driving and 51 miles per gallon in highway driving. The car is driven 447 miles on 9 gallon of gasoline. How many miles were driven in the city and how many were driven on the highway?
49 miles/gal = city rate
51 miles/gal = highway rate
447 miles/9 gal is how much you drove...
(city mileage)/(city rate) + (highway mileage)/(highway rate) = 9 gal.
Set up a problem with variables or use a guess-and-check approach.
153 miles highway and 294 miles city.
To determine how many miles were driven in the city and on the highway, we need to solve a system of equations using the given information.
Let's assume that x represents the number of miles driven in the city and y represents the number of miles driven on the highway.
From the given information, we can set up the following equations:
Equation 1: x + y = 447 (total miles driven)
Equation 2: (x/49) + (y/51) = 9 (total gallons of gasoline used)
In Equation 2, we divide the distances driven in the city and on the highway by their respective fuel efficiency to get the total number of gallons used. We then set this equal to 9, the total number of gallons used.
To solve this system of equations, we can use a method called substitution.
Solving Equation 1 for x, we get:
x = 447 - y
Substituting this value of x into Equation 2, we have:
((447 - y)/49) + (y/51) = 9
Now we can solve for y:
Multiply both sides of the equation by their common denominator of 49*51:
(447 - y) * 51 + 49y = 9 * 49 * 51
Expanding and simplifying:
22,797 - 51y + 49y = 22,491
Combine like terms:
-2y = 22,491 - 22,797
-2y = -306
Divide both sides by -2:
y = -306 / -2
y = 153
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 153 = 447
x = 447 - 153
x = 294
Therefore, 294 miles were driven in the city and 153 miles were driven on the highway.