Answer:
Time (secs) => distance (ft)
1 => ⅔
15 => 10
24 => 16
45 => 30
Step-by-step explanation:
Equation to represent this proportional relationship is
, 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.
![d = tk](https://tex.z-dn.net/?f=%20d%20%3D%20tk%20)
![16 = 24k](https://tex.z-dn.net/?f=%2016%20%3D%2024k%20)
(division property of equality)
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):
![d = tk](https://tex.z-dn.net/?f=%20d%20%3D%20tk%20)
![d = 1*\frac{2}{3}](https://tex.z-dn.net/?f=%20d%20%3D%201%2A%5Cfrac%7B2%7D%7B3%7D%20)
d = ⅔ ft
For 10 ft, let's find the time (t) taken:
![d = tk](https://tex.z-dn.net/?f=%20d%20%3D%20tk%20)
![10 = t*\frac{2}{3}](https://tex.z-dn.net/?f=%2010%20%3D%20t%2A%5Cfrac%7B2%7D%7B3%7D%20)
Multiply both sides by 3
![10*3 = t*\frac{2}{3}*3](https://tex.z-dn.net/?f=%2010%2A3%20%3D%20t%2A%5Cfrac%7B2%7D%7B3%7D%2A3%20)
![30 = t*2](https://tex.z-dn.net/?f=%2030%20%3D%20t%2A2%20)
Divide both sides by 2
![\frac{30}{2} = \frac{t*2}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%7D%7B2%7D%20%3D%20%5Cfrac%7Bt%2A2%7D%7B2%7D%20)
![15 = t](https://tex.z-dn.net/?f=%2015%20%3D%20t%20)
t = 15 secs
For 45 secs, let's find distance (d):
![d = tk](https://tex.z-dn.net/?f=%20d%20%3D%20tk%20)
![d = 45*\frac{2}{3} = 15*2](https://tex.z-dn.net/?f=%20d%20%3D%2045%2A%5Cfrac%7B2%7D%7B3%7D%20%3D%2015%2A2)
d = 30 ft