Question

Willow is driving on the freeway. She just passed mile marker 325 . The markers have been increasing as she drives by them. The fastest Willow will drive is 75 miles per hour. However, there is a bit of traffic that might slow her down, but she doesn't know exactly how much it will slow her down. Select an inequality that represents Willow's position relative to the mile markers two hours from now.

a) 325+2r≤475
b) 325+2r≥475
c) 325+2r≤753
d) 25+2r≥75​

Answer 1

The correct inequality to represent Willow's position after two hours on the freeway, given a maximum speed of 75 miles per hour and potential traffic delays, is 325 + 2r ≤ 475.

Step-by-step explanation:

The question involves creating an inequality that represents Willow's position after driving on the freeway for two hours from mile marker 325. Given that her maximum speed is 75 miles per hour and that traffic may slow her down, we can use the rate 'r' to represent her average speed during the next two hours. As she will not be driving faster than 75 miles per hour, the inequality is set up with a maximum possible distance in mind.

After two hours, if she travels at her maximum speed of 75 miles per hour, she would have traveled 2 hours × 75 miles per hour = 150 miles. So she will be at least at mile marker 325 + 150 = 475. However, because traffic can slow her down, this is the upper limit of where she could be, which means the correct inequality representing her position relative to the mile markers after two hours would be:

325 + 2r ≤ 475,

where 'r' is her average speed during the two hours. This inequality assumes that 'r' will be less than or equal to 75 miles per hour because she cannot exceed her fastest driving speed due to traffic conditions.