Question

Lorrie biked d miles in 2 hours. She traveled at an average speed of more than 8 miles per hour. To determine the distance she may have traveled, she uses the inequality 2d > 8. She then determines that she biked at most 4 miles. Analyze Lorrie’s inequality and solution.

Answer 1

`\fbox{\begin{minipage}{14em}Lorrie's inequality is incorrect\end{minipage}}`

`\fbox{\begin{minipage}{16em}The solution is: d is greater than 16\end{minipage}}`

Explanation:

Step 1: Define the problem

Given:

Lorrie biked
`d` miles in time
`t = 2` hours.

Lorrie traveled at speed
`s` which is greater than
`8` (mile/hour).

Task:

Lorrie wants to determine the distance she may have traveled.

Key point:

The relation among the distance biked
`d`, time
`t`, and the speed
`s` is represented:

`d = s` x
`t`

Step 2: Substitute given data into the main relation

with:
`s > 8` and
`t = 2`

=>
`d = s` x
`t`

=>
`d` >
`8` x
`2`

Simplify:

`d > 16`

Step 3: Verify Lorrie's inequality

Lorrie uses the inequality
`2d > 8` to conclude that she traveled a distance
`d` at most
`4` miles, or
`d < 4`.

Considering the correct answer is at step 2, in which,
`d > 16`.

=> Lorrie's conclusion is incorrect.

Hope this helps!

:)

Answer 2

Lorrie should have used division in the inequality instead of multiplication. She would have determined that she biked more than 16 miles instead of at most 4 miles.

Explanation:

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