Question

HURRY GIVING 64 POINTS 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

HURRY GIVING 64 POINTS 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 2

The distance travelled by her must be greater than 16 miles.

Explanation:

Her inequality is comparing the time she travelled multiplied by the distance with her speed, therefore it's not a valid expression to determine what she wants to know. Even if that was right, she made a mistake when she made the conclusion that the distance travelled was "at most" 4 miles, since by the inequality it should be "more than" 4 miles.

To do that, we need to look at the expression for speed, which is shown below:

speed = distance/time

We have her stimated speed and the time it took her to travel "d" miles, then a better inequality to guess the value for "d" would be:

d/2 > 8

Because then we are comparing variables of the same nature, speed and speed. We know that her actual speed was more than 8, therefore the expression to the left must be greater than that. In order to solve it we need to isolate the "d" variable.

d > 2*8

d > 16 miles

The distance travelled by her must be greater than 16 miles.