Question

I need help with this word problem I suck at word problems

Answer 1

We have the given equation that represents the distance D from home after x hours of driving:

a)

To graph the equation, we use the distance on the y-axis and the hours on the x-axis.

We need to find the points:

When x=1,

`\begin{gathered} D=1600-100x \\ D=1600-100(1) \\ D=1500 \\ \text{Hence, we have the point (1,1500)} \end{gathered}`

When x=2,

`\begin{gathered} D=1600-100x \\ D=1600-100(2) \\ D=1400 \\ \text{Hence, we have the point (2,1400)} \end{gathered}`

When x=3

`\begin{gathered} D=1600-100x \\ D=1600-100(3) \\ D=1300 \\ \text{Hence, we have the point (3,1300)} \end{gathered}`

When x=4

`\begin{gathered} D=1600-100x \\ D=1600-100(4) \\ D=1600-400 \\ D=1200 \\ \text{Hence, we have the point (4,1200)} \end{gathered}`

When x= 5

`\begin{gathered} D=1600-100x \\ D=1600-100(5) \\ D=1100 \\ \text{Hence, we have the point (5,1100)} \end{gathered}`

Plot the points to get the graph.

b) The slope is given by the rate of change, in this case, the range of change is 100 because this number depends on x. where x represents the number of hours.

c) If Jim is driving after 6 hours, then, we need to replace x = 6 on the distance equation.

Hence:

`\begin{gathered} D=1600-100x \\ D=1600-100(6) \\ D=1000 \end{gathered}`

Therefore, after 6 hours Jim is 1000km far away from home.