Helppppp anyone please math

Question

Gary and Alex live different distances from their school. They both leave home at the same time. Gary bicycles to school. His distance from the school in miles,d, as a function of t, time in minutes, is given by this equation.

d=-1/5t+5

Alex skateboards to school. The table shows his distance from school at different times.

(Alex skateboards to school) Time since leaving home in minutes and Distance from school in miles

6 and 2.5

12 and 2.0

18 and 1.5

which boy arrives at school first? how many minutes before the other boy arrives? Show your work.

Answer 1

Gary's distance from school is...

d₁ = -1/5t + 5

Gary arrives to school when d₁ = 0. So...

d₁ = -1/5t + 5 = 0

-1/5t = - 5

-5·(-1/5t) = -5·(-5)

t = 25 minutes

For Alex, you may see a pattern:

6 and 2.5

12 and 2.0

18 and 1.5

Looking at the numbers going down in order:

6... 12... 18... Next number is 24 and 0 must be the number before the 6. So...

0... 6... 12... 18... 24 is the pattern. Notice that these numbers represent the time Alex has been walking.

Look at this pattern now... 2.5... 2.0... 1.5... Looks like decreasing by 0.5. That means:

3.0... 2.5.. 2.0... 1.5... 1.0... must be the previous number and the next number in the pattern. Just like with Gary, when distance is 0, Alex is at school. What is the time that is paired with 0? Continue the pattern...

0 and 3.0

6 and 2.5

12 and 2.0

18 and 1.5

24 and 1.0

30 and 0.5

36 and 0

Since the distance is 0 when time is 36 minutes, it must take Alex 36 minutes to get to school. This means that Gary gets to school first and he is there 36 - 25 = 11 minutes earlier.