contestada

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.

Respuesta :

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.

MrRoyal

Inequalities are used to represent unequal expressions.

  • The inequality expression that shows when Aisha will be ahead is [tex]55x > 50x + 15[/tex].
  • The solution to the inequality is [tex]x > 3[/tex]

Let

[tex]D \to[/tex] Distance

From the complete question, we have:

[tex]D_A = 55x[/tex] --- Aisha's distance after x hours

[tex]D_L = 50x + 15[/tex] ---- Luke's distance after x hours. (The 15 implies that Luke has travelled 15 miles, before Aisha begin her trip)

Aisha will be ahead Luke, when:

[tex]D_A > D_L[/tex]

So, we have:

[tex]55x > 50x + 15[/tex]

Collect like terms

[tex]55x - 50x > 15[/tex]

[tex]5x > 15[/tex]

Divide both sides by 5

[tex]x > 3[/tex]

This means that Aisha will be ahead, after 3 miles.

Read more about inequalities at:

https://brainly.com/question/17675534

Otras preguntas