Answer:
Malcom's family travel 15 miles per hour faster than Theo's
Step-by-step explanation:
See attachment for complete question
Given
Malcom's Family:
[tex]d = 65t[/tex]
To determine the equation of Theo's family, we refer to the attached graph.
From the graph:
[tex]t = 1; d = 50[/tex]
[tex]t = 2; d = 100[/tex]
First, we determine the slope, m:
[tex]m = \frac{d_2 - d_1}{t_2 - t_1}[/tex]
[tex]m = \frac{100 - 50}{2- 1}[/tex]
[tex]m = \frac{50}{1}[/tex]
[tex]m = 50[/tex]
Next, we determine equation for Theo's family using:
[tex]d - d_1 = m(t - t_1)[/tex]
[tex]d - 50 =50(t - 1)[/tex]
[tex]d - 50 =50t - 50[/tex]
Add 50 to both sides
[tex]d - 50 +50=50t - 50 + 50[/tex]
[tex]d =50t[/tex]
So, we have the following:
[tex]d = 65t[/tex] --- For Malcom's family
This implies that Malcom's family travel at 65 miles per hour
[tex]d =50t[/tex] --- For Theo's family
This implies that Theo's family travel at 50 miles per hour
The difference between this rates is:
[tex]Rate = 65t - 50t[/tex]
[tex]Rate = 15t[/tex]
Which implies that Malcom's family travel 15 miles per hour faster than Theo's
