Question

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

The equation d = 65t models the distance, d, that Malcolm's family travels after t hours.
The graph below shows the relationship between the distance and the amount of time that Theo's family traveled.

Answer 1

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

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 = (d_2 - d_1)/(t_2 - t_1)`

`m = (100 - 50)/(2- 1)`

`m = (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