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​ 55 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.

Answer 1

Speed of Luke while driving=50 miles per hour

Speed of Aisha while driving=55 miles per hour

⇒After x hours

Distance =Speed × Time

Distance travelled by luke after x hours =50x mile

Distance travelled by Aisha after x hours =55x mile

We will find common multiple of 50 and 55 which is 550.

So, After 11 hours luke will cover 550 miles and after 10 hours Aisha will cover 550 miles.

So, Aisha will be always ahead of Luke if their speeds are 55 miles per hour and 50 miles per hour respectively on the highway.

So, 55x>50x.

Answer 2

If x is the time, in hours, then:

x(55)=x(50)+15

5x=15

x=3 hours before Aisha is ahead of Luke

hope this helps you!