Question

Jessica Reads a story about a turtle that swam 16 feet in 24 seconds. She assumes that the time that it takes the turtle to swim a distance of d feet is a proportional relationship. Jessica starts to create the table shown for other times and distances the turtle swam. Enter the missing numbers in the tableto represent the proportional relationship

Answer 1

Time (secs) => distance (ft)

1 => ⅔

15 => 10

24 => 16

45 => 30

Explanation:

Equation to represent this proportional relationship is
`d = tk`, 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`

`16 = 24k`

`(16)/(24) = k` (division property of equality)

`(2)/(3) = k`

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`

`d = 1*(2)/(3)`

d = ⅔ ft

For 10 ft, let's find the time (t) taken:

`d = tk`

`10 = t*(2)/(3)`

Multiply both sides by 3

`10*3 = t*(2)/(3)*3`

`30 = t*2`

Divide both sides by 2

`(30)/(2) = (t*2)/(2)`

`15 = t`

t = 15 secs

For 45 secs, let's find distance (d):

`d = tk`

`d = 45*(2)/(3) = 15*2`

d = 30 ft