Gina and Derek saw some trees on their walk through the park. They made a diagram to show the distance between trees.

A line diagram shows 5 points. The points are labeled start, maple tree, oak tree, pine tree, and end. The distance from the start to the maple tree is 5 yards. The distance from the maple tree to the end is 28 and two-sixths yards. The distance from the oak tree to the pine tree is 11 and three-sixths yards. The distance from the pine tree to the end is 7 and five-sixths yards.

Select the equation that calculates the distance between the maple tree and the oak tree.

(1 point)
Responses

5+1136+756=2426
yards

5 + 11 3 6 + 7 5 6 = 24 2 6 yards

2826−5=2326
yards

28 2 6 - 5 = 23 2 6 yards

2826−(1136−756)
= 2446
yards

28 2 6 - 11 3 6 - 7 5 6 = 24 4 6 yards

2826−(1136+756)
= 9
yards

28 2 6 - 11 3 6 + 7 5 6 = 9 yards

1 answer

To find the distance between the maple tree and the oak tree, we need to first determine the overall distance from the start to the oak tree.

  1. The total distance from the start to the maple tree is 5 yards.
  2. The distance from the maple tree to the end is 28 and two-sixths yards.
  3. The distance from the oak tree to the pine tree is 11 and three-sixths yards.
  4. The distance from the pine tree to the end is 7 and five-sixths yards.

Let's calculate the total distance from the start to the end and find the position of the oak tree.

The distance from the start to the end is: \[ 5 + 28\frac{2}{6} = 5 + 28.3333\ldots = 33.3333\ldots \text{ yards} \]

Now, we can also consider the distance from the oak tree:

  • The distance from the oak tree to the pine tree is \( 11\frac{3}{6} = 11.5 \) yards.
  • The distance from the pine tree to the end is \( 7\frac{5}{6} = 7.8333\ldots \) yards.

Calculating the distance from the oak tree to the end: \[ 11\frac{3}{6} + 7\frac{5}{6} = 11.5 + 7.8333\ldots = 19.3333\ldots \text{ yards} \]

The total distance from the start to the end is \( 33.3333\ldots\) yards. Now, we can find the distance from the maple tree to the oak tree:

  1. From the start to the maple tree: 5 yards
  2. From the start to the oak tree:
  • Start to Maple: 5 yards
  • Maple to Oak: distance to be determined (which we are trying to find)

The equation for the distance between the maple tree and the oak tree involves the total distance from the end and the distances to the other trees. The equation that directly represents this is: \[ 28 \frac{2}{6} - 5 = 23 \frac{2}{6} \text{ yards} \]

None of the questions provided the answer exactly as "5 + 11 \frac{3}{6} + 7 \frac{5}{6} = 24 \frac{2}{6} \text{ yards}" calculates distance explicitly, but the most relevant one that calculates the distance from the maple tree to the oak tree is the response:

28 \frac{2}{6} - 5 = 23 \frac{2}{6} yards.