Patty went to 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 has to be written as a linear equation
If she drove x km at 100 km/hr, then the rest (260-x) was at 80 km/hr
since time = distance/speed, just add up the times for each part:
x/100 + (260-x)/80 = 11/4
(2 hr 45 min = 2 3/4 hours)
Sure, let me try to put this in a linear equation for you:
Let's say x represents the time in hours Patty drove on the 100 km/h highway, and y represents the time in hours she drove on the 80 km/h roads.
We know that the total time Patty drove is 2 hours and 45 minutes, which is equivalent to 2.75 hours.
Since Patty drove a certain distance on the highway and a certain distance on the roads, we can create the following equation:
100x + 80y = 260
This equation represents that the total distance Patty drove on the 100 km/h highway (100x) plus the total distance she drove on the 80 km/h roads (80y) equals 260 km.
I hope this equation drives your curiosity!
To write this as a linear equation, let's assign variables to the unknown quantities.
Let:
x = distance in kilometers covered on the 100 km/h highway
y = distance in kilometers covered on the 80 km/h roads
Now, let's convert the time into hours.
The total time taken for the journey is 2 hours and 45 minutes. Since there are 60 minutes in an hour, 45 minutes is equal to 45/60 = 0.75 hours.
The time taken on the highway is x/100 hours since the speed is 100 km/h.
The time taken on the 80 km/h roads is y/80 hours since the speed is 80 km/h.
The total time taken for both parts of the journey is given as 2 hours and 45 minutes, which can be written as 2.75 hours.
So, the equation representing the total distance traveled is:
x/100 + y/80 = 2.75
This is the linear equation representing Patty's journey.
To write this as a linear equation, we need to understand the relationship between the distance Patty drove and the time it took her.
Let's start with the distance she drove on the highway, which we will represent as x. Since the speed limit on the highway is 100 km/h, Patty's time taken while driving on the highway will be x/100 hours.
Now, let's consider the distance she drove on the 80 km/h roads. The total distance she drove was 260 km, and she drove x km on the highway. So, the distance she drove on the 80 km/h roads would be 260 - x km. Since the speed on the 80 km/h roads is 80 km/h, Patty's time taken while driving on these roads will be (260 - x)/80 hours.
Patty's total driving time is given as 2 hours and 45 minutes, which is equivalent to 2.75 hours.
Finally, we can write the linear equation by equating the total driving time with the sum of the time taken on the highway and the time taken on the 80 km/h roads:
x/100 + (260 - x)/80 = 2.75
Simplifying this equation will give us the final linear equation.