Answer:
Time (secs) => distance (ft)
1 => ⅔
15 => 10
24 => 16
45 => 30
Step-by-step explanation:
Equation to represent this proportional relationship is [tex] d = tk [/tex], where,
t = time
d = distance
k = constant of proportionality
To complete the table, let's find k given that the turtles swarm 16 ft (d) in 24 secs (t).
Substitute d = 16, t = 24 into the equation.
[tex] d = tk [/tex]
[tex] 16 = 24k [/tex]
[tex] \frac{16}{24} = k [/tex] (division property of equality)
[tex] \frac{2}{3} = k [/tex]
Let's complete the table by substituting the value of k and the other given value of t or d, as the case may be:
For 1 sec, let's find distance (d):
[tex] d = tk [/tex]
[tex] d = 1*\frac{2}{3} [/tex]
d = ⅔ ft
For 10 ft, let's find the time (t) taken:
[tex] d = tk [/tex]
[tex] 10 = t*\frac{2}{3} [/tex]
Multiply both sides by 3
[tex] 10*3 = t*\frac{2}{3}*3 [/tex]
[tex] 30 = t*2 [/tex]
Divide both sides by 2
[tex] \frac{30}{2} = \frac{t*2}{2} [/tex]
[tex] 15 = t [/tex]
t = 15 secs
For 45 secs, let's find distance (d):
[tex] d = tk [/tex]
[tex] d = 45*\frac{2}{3} = 15*2[/tex]
d = 30 ft
