Answer:
Faster mode: Car
Less time: 0.93 hour
Step-by-step explanation:
Given
[tex]y = 55x[/tex] --- The equation of travelling by car
See attachment for missing details
Required
Determine by how much less time Lisa will travel 231 miles using the faster mode
First, we calculate the equation of travelling by train.
Start by calculating the slope (m)
[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (2,90)[/tex]
[tex](x_2,y_2) = (4,180)[/tex]
[tex]m = \frac{180 - 90}{4-2}[/tex]
[tex]m = \frac{90}{2}[/tex]
[tex]m = 45[/tex]
The equation is then calculated using:
[tex]y = m(x - x_3) + y_3[/tex]
Where
[tex](x_3,y_3) = (6,270)[/tex]
[tex]y = 45(x - 6) + 270[/tex]
[tex]y = 45x - 270 + 270[/tex]
[tex]y = 45x[/tex]
So, we have:
[tex]y = 55x[/tex] --- The equation of travelling by car
[tex]y = 45x[/tex] --- The equation of travelling by train
Next, we calculate the speed travelled using both means for 231 miles.
For travelling by car: Substitute 231 for y in [tex]y = 55x[/tex]
[tex]231 = 55 * x[/tex]
[tex]x = \frac{231}{55}[/tex]
[tex]x = 4.20[/tex]
By car, Lisa travels for 4.20 hours
For travelling by train: Substitute 231 for y in [tex]y = 45x[/tex]
[tex]231 = 45 * x[/tex]
[tex]x = \frac{231}{45}[/tex]
[tex]x = 5.13[/tex]
By train, Lisa travels for 5.13 hours
So, the faster mode of transportation is the car:
The less time is:
[tex]5.13 - 4.20 =0.93\ hour[/tex]
The less time spent is 0.93 hour
