Question

Malcolm and Theo's families are both traveling to the same vacation resort.

Answer 1

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:

$d = 65t$

To determine the equation of Theo's family, we refer to the attached graph.

From the graph:

$t = 1; d = 50$

$t = 2; d = 100$

First, we determine the slope, m:

$m = \frac{d_2 - d_1}{t_2 - t_1}$

$m = \frac{100 - 50}{2- 1}$

$m = \frac{50}{1}$

$m = 50$

Next, we determine equation for Theo's family using:

$d - d_1 = m(t - t_1)$

$d - 50 =50(t - 1)$

$d - 50 =50t - 50$

Add 50 to both sides

$d - 50 +50=50t - 50 + 50$

$d =50t$

So, we have the following:

$d = 65t$ --- For Malcom's family

This implies that Malcom's family travel at 65 miles per hour

$d =50t$ --- For Theo's family

This implies that Theo's family travel at 50 miles per hour

The difference between this rates is:

$Rate = 65t - 50t$

$Rate = 15t$

Which implies that Malcom's family travel 15 miles per hour faster than Theo's