Question

This graph shows the distance vs. time relationship for the Lane 1 and Lane 2 turtles. Here are their equations:

Lane 1: d= 6+ 1t
Lane 2: d = 3t
Select all of the true statements.
(Select all that apply.)
1. The Lane 2 turtle is faster than the Lane 1 turtle.
2. At 3 seconds, the turtle in Lane 2 is 12 feet from the start.
3. At 12 seconds, the turtle in Lane 1 is 6 feet from the start.
4. The Lane 1 turtle has a head start.

Answer 1

True statements are:

(i) The lane 2 turtle is faster than the lane 1 turtle.

(iv) The lane 1 turtle has a head start.

Explanation:

Now we proceed to check the value of truth for each choice:

(i) The lane 2 turtle is faster than the lane 1 turtle.

Speed of the turtle is the slope of the linear function, the greater the slope, the faster the turtle. Hence, the lane 2 turtle is faster than the lane 1 turtle. (Answer: TRUE)

(ii) At 3 seconds, the turtle in Lane 2 is 12 feet from start.

Let the position of the turtle in Lane 2 be represented by
`d = 3\cdot t`. For
`t = 3\,s`, then
`d = 3\cdot (3) = 9`. Hence, the turtle in Lane 2 is just 9 feet from the start. (Answer: FALSE)

(iii) At 12 seconds, the turtle in Lane 1 is 6 feet from the start.

Let the position of the turtle in Lane 1 be represented by
`d = 6 + t`. For
`t = 12\,s`, then
`d = 6+12 = 18`. Hence, the turtle is 12 feet from the start. (Answer: FALSE)

(iv) The lane 1 turtle has a head start.

According to graph, Lane 1 turtle starts at a position of 6 feet, whereas Lane 2 turtle start at a position of 0 feet. Hence, Lane 1 turtle has a head start. (Answer: TRUE)