Question

Question 5

Kayleigh and Allison race. Kayleigh runs 5 miles per hour. Allison runs 3 miles per hour but has a 1 mile head
start. Using the formulas below where h is hours and d is distance, how long does it take before they meet
each other in the race?
Kayleigh d = 5h
Allison d = 3h+1

Answer 1

Let's call the time it takes for Kayleigh and Allison to meet each other "t".

We know that Kayleigh runs at a constant rate of 5 miles per hour, so the distance she covers in "t" hours is given by:

Kayleigh's distance = Kayleigh's speed * time = 5t

Allison runs at a constant rate of 3 miles per hour, but she has a 1 mile head start. This means that by the time Kayleigh and Allison meet each other, Allison will have run "t" hours minus the time it took her to cover her head start distance. The time it takes Allison to cover her head start distance is:

Time for Allison's head start = distance / speed = 1 / 3 = 0.33 hours (rounded to two decimal places)

Therefore, when Kayleigh and Allison meet each other, Allison will have run:

Allison's distance = Allison's speed * (t - 0.33) = 3(t - 0.33)

Now, we know that when they meet, Kayleigh's distance is equal to Allison's distance:

Kayleigh's distance = Allison's distance

5t = 3(t - 0.33)

Simplifying and solving for "t", we get:

5t = 3t - 1

2t = 1

t = 0.5

Therefore, it takes Kayleigh and Allison 0.5 hours (or 30 minutes) to meet each other in the race.