Patty went to visit her cousins for the weekend. She drove 260 km in 2 h 45 min, some of it on a 100 km/h highway and the rest on 80 km/h roads.
THIS ANSWER MUST BE ANSWERED AS A LINEAR SYSTEM OF EQUATIONS
distance on the faster hiway --- x km
distance on the slower hiway --- y
x + y = 260
x/100 + y/80 = 11/4
each term times 400
4x + 50y = 1100
take it from there to solve for x and y
Let's use the following variables to solve this problem:
Let x be the distance (in km) Patty drove on the 100 km/h highway.
Let y be the distance (in km) Patty drove on the 80 km/h roads.
We know that Patty drove a total distance of 260 km, so we can write the first equation:
x + y = 260
We also know that Patty drove for a total of 2 hours and 45 minutes, or 2.75 hours. We can use this information to determine the time it took to drive on the highway and the time it took to drive on the 80 km/h roads.
The time it took Patty to drive on the highway can be calculated as x divided by the speed (100 km/h):
x / 100
The time it took Patty to drive on the 80 km/h roads can be calculated as y divided by the speed (80 km/h):
y / 80
The total time Patty drove can be expressed as the sum of the time on the highway and the time on the 80 km/h roads:
x / 100 + y / 80 = 2.75
So, the system of linear equations that represents this problem is:
x + y = 260
x / 100 + y / 80 = 2.75
Solving this system of equations will give the values of x and y, representing the distances Patty drove on the highway and the 80 km/h roads, respectively.
To solve this problem using a linear system of equations, let's represent the distance travelled on the highway as "x" and the distance travelled on the roads as "y".
According to the problem, the total distance travelled is 260 km. So we can write the equation:
x + y = 260 --(1)
Also, we know that Patty traveled on the highway at a speed of 100 km/h, for the time she spent on the highway. We can use the equation:
x/100 = (actual time spent on the highway in hours) --(2)
Similarly, Patty traveled on the roads at a speed of 80 km/h, for the time spent on the roads. We can use the equation:
y/80 = (actual time spent on the roads in hours) --(3)
Now, let's convert the given time into hours. Patty spent 2 hours and 45 minutes, which is equal to 2.75 hours. So we can replace the actual time spent on the highway and the roads in equations (2) and (3) respectively.
Substituting these values into the equations, we can solve the system to find the values of x and y.
x/100 + y/80 = 2.75
Now, we have a system of equations:
x + y = 260
x/100 + y/80 = 2.75
Solving this system of equations will give us the values of x and y, which represent the distances travelled on the highway and the roads respectively.