Question

luke and aisha are traveling on the same road in the same direction. luke is driving at a rate of 50 miles per hour, and aisha is driving at a rate of 56 miles per hour. write and solve an inequality to find when aisha will be ahead of luke on the highway. let x represent time in hours. how can you validate your results? explain
the inequality □ represents this situation.
(type an inequality using x as the variable. do not simplify.)

Explanation:

Step1: Set up the inequality

The distance formula is \(d = vt\) (where \(d\) is distance, \(v\) is velocity, and \(t\) is time). Luke's speed \(v_{Luke}=50\) miles per hour, so his distance \(d_{Luke}=50x\). Aisha's speed \(v_{Aisha} = 56\) miles per hour, so her distance \(d_{Aisha}=56x\). We want to find when \(d_{Aisha}>d_{Luke}\), so the inequality is \(56x>50x\).

Step2: Solve the inequality

Subtract \(50x\) from both sides: \(56x - 50x>50x-50x\).
Simplify: \(6x>0\).
Divide both sides by \(6\): \(x > 0\).

Answer:

The inequality is \(56x>50x\). When we solve it, we subtract \(50x\) from both sides to get \(6x>0\), and then divide by \(6\) to find \(x>0\). This means that as long as the time \(x\) (in hours) is greater than \(0\) (i.e., when they start traveling), Aisha will be ahead of Luke. Because Aisha's speed (\(56\) miles per hour) is greater than Luke's speed (\(50\) miles per hour), over any positive amount of time, Aisha will cover more distance.