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Trail

Mohawk: 6.8 distance (miles)
Ranger Cove: 4.8 distance (miles)
Willow Oak: 5.7 distance (miles)
It took Lannie 1.9 hours to hike Ranger Cove Trail. Which of the following equations could help you find the average hiking rate for Lannie?
1. 1.9/4.8=X
2. 4.8x =1.9
3. 1.9x =4.8
4. x=1.9 times 4.8

Part 2:
It took Ava 4 hours to hike Mohawk Trail. Which of the following equations could help you find the average hiking rate for Ava?
1. 6.8x=4
2. 4x =6.8
3. 4/6.8=x
4. x/6.7=4

11 answers

To find the average hiking rate, you can use the formula:

\[ \text{Average Rate} = \frac{\text{Distance}}{\text{Time}} \]

Part 1:

For Lannie, we know:

  • Distance for Ranger Cove Trail = 4.8 miles
  • Time taken = 1.9 hours

Using the average rate formula, we have:

\[ x = \frac{4.8}{1.9} \]

This means we can rearrange it as:

\[ 1.9x = 4.8 \]

So, the correct equation from the options provided for Lannie is: 3. 1.9x = 4.8

Part 2:

For Ava, we know:

  • Distance for Mohawk Trail = 6.8 miles
  • Time taken = 4 hours

Again, using the average rate formula, we have:

\[ x = \frac{6.8}{4} \]

This can be rearranged to:

\[ 4x = 6.8 \]

So, the correct equation from the options provided for Ava is: 2. 4x = 6.8

This question has two parts. First, answer Part A. Then, answer Part B.
Part A
The level of the Green River rises by 0.75 foot each hour during a heavy rainstorm. After several hours, the level of the river changed by 3.75 feet.
Which equation could be used to determine the number of hours since the rainstorm began?
1. h/0.75=3.75
2. 0.75h =3.75
3. h+0.75=3.75
4. h-0.75=3.75

Part B:
How many hours has it been since the rainstorm began?

Part A:

To determine the number of hours since the rainstorm began, we can use the relationship between the rise in the river level, the rate at which it rises, and the time.

The level of the river rises by 0.75 feet each hour, and after several hours, it changed by 3.75 feet. The equation that models this situation is:

\[ 0.75h = 3.75 \]

So, the correct equation from the options provided is: 2. 0.75h = 3.75

Part B:

To find the number of hours (h), we can solve the equation:

\[ 0.75h = 3.75 \]

Divide both sides by 0.75:

\[ h = \frac{3.75}{0.75} \]

Calculating this gives:

\[ h = 5 \]

Therefore, it has been 5 hours since the rainstorm began.

Find the Error A student solved 1x = - 40:
1/2x÷ 2=-40÷2
x=-20
Find the student's mistake and correct it.
The student (options: divided each side by 2, subtracted 2 from each side, added 2 to each side, multiplied each side by 2.) The student should have (options: subtracted 2 from each side,multiplied each side by 2,
divided each side by 2,added 2 to each side) The correct answer is x= (options: -10, -20, -40, -80)

Let's analyze the problem step-by-step.

The original equation given was: \[ 1x = -40 \]

The student seems to have transformed this equation incorrectly as follows: \[ \frac{1}{2}x \div 2 = -40 \div 2 \]

  1. Identify the student's mistake:
    • The equation \( 1x = -40 \) was incorrectly manipulated to \( \frac{1}{2}x \div 2 = -40 \div 2 \).
    • The student divided the left side of the equation by 2 incorrectly. The initial step should maintain the correct manipulation.

Therefore, the student's mistake is: divided each side by 2.

  1. What the student should have done:
    • To correctly solve the equation, the student could simply evaluate 1x = -40 directly. There is no need to manipulate it by dividing, multiplying, or adding since it can be simplified directly.
    • Thus, no operation is strictly needed, but if we want to correct it instead of simply stating x = -40, they could have kept it simple by multiplying by 1 (essentially doing nothing), which leads us back to just saying \( x = -40 \).

However, if we consider their intent to create equivalent transformations that align, we would state they should have multiplied each side by 1 for the sake of argument. There would be no actual necessary operation.

  1. The correct answer: The original equation \( 1x = -40 \) simplifies directly to \( x = -40 \).

Thus the final options would be:

  • Student's Mistake: divided each side by 2.
  • The student should have: done nothing essential or kept it unmodified but for affirmational purposes, could be considered multiplied each side (if contextually relevant).
  • The correct answer is: x = -40.

In summary:

  • Mistake: Divided each side by 2
  • Should have: done nothing or, to justify answer paths, multiplied each side by 1.
  • Correct Answer: x = -40.
its wrong, please use the options provided

Thank you for your patience. Let's properly analyze the problem using just the options provided.

Given Information

  1. The original equation: \( 1x = -40 \)
  2. The student's manipulation: \[ \frac{1}{2}x \div 2 = -40 \div 2 \] followed by: \[ x = -20 \]

Identifying the Mistake:

Let's break down the student's operation.

  • The student seems to have incorrectly concluded that \( \frac{1}{2}x \) somehow results from \( 1x \).
  • It looks like they divided both sides by 2, which was unnecessary.

Therefore, the student divided each side by 2.

What the Student Should Have Done:

To find \( x \) from \( 1x = -40 \), the student should have simply kept the equation as it is or multiplied it by 1 if we must assume they needed a transformation.

Since multiplying was not provided as an option relevant to "what they should have done", the most fitting option remaining is for their actual operation, and they should have instead solved directly.

However, given your options:

  • If they were to do something, they could have multiplied by 2 to avoid entering fractions or mismanipulation.

Thus, the answer is:

  • The student should have: multiplied each side by 2.

Correct Answer:

From the original equation: \[ x = -40 \] The correct answer is:

  • \( x = -40. \)

Summary:

  • Student's mistake: divided each side by 2.
  • The student should have: multiplied each side by 2.
  • The correct answer is: x = -40.
its wrong again, please redo it

I apologize for the confusion earlier! Let's clarify the steps and correctly identify the mistakes using only the options provided.

Given

  • The original equation: \( 1x = -40 \)

Student's Incorrect Method:

  • The student wrote: \[ \frac{1}{2}x \div 2 = -40 \div 2 \]
  • The student arrived at \( x = -20 \).

Analyzing the Mistake:

  1. The student incorrectly manipulated the equation. Instead of correctly solving \( 1x = -40 \), they introduced an unnecessary division by 2.
  2. Hence, the error they made was: divided each side by 2.

What the Student Should Have Done:

  • Since we want to solve for \( x \) from \( 1x = -40 \), there was no need for division. But given the options available, in hindsight, to get to the solution correctly from the start:
  • The student should have simply solved for \( x \) directly, leading us to note that they could have equivalently manipulated it without wrongful reduction.

However, if they had been asked to transform it for correctness, they could:

  • They should multiply each side by 1 instead of erroneous division, but since that option doesn't exist, the best assumption would be they should have multiplied each side by 1 (sticking to original).

Correct Answer:

  • From the original equation \( 1x = -40 \), the correct answer is:
  • x = -40.

Summary:

  • The student's mistake: divided each side by 2.
  • The student should have: multiplied each side by 1 (but since this is to clarify, let's frame everything under the bounds of solving appropriately).
  • The correct answer is: x = -40.

Again, I apologize for the earlier confusion. Thank you for your patience.

1/2x =-40

Thank you for your clarification. Let's solve the equation \( \frac{1}{2}x = -40 \) step-by-step.

Step 1: Identify the Mistake

It seems like we are working from a new equation, \( \frac{1}{2}x = -40 \).

  1. The student attempted to manipulate the equation incorrectly by using \( \frac{1}{2}x ÷ 2 = -40 ÷ 2 \).
  2. This is not a correct transformation of the original equation. The operation should maintain the balance of the equation.

Student’s Mistake

The student divided each side by 2, which was not the correct approach to solving the equation directly.

Correct Steps to Solve \( \frac{1}{2}x = -40 \):

To isolate \( x \), you should multiply both sides by 2 instead of dividing.

  1. Start with: \[ \frac{1}{2}x = -40 \]

  2. Multiply both sides by 2: \[ 2 \times \frac{1}{2}x = 2 \times -40 \]

  3. This simplifies to: \[ x = -80 \]

Final Answers:

  • The student's mistake: divided each side by 2.
  • The student should have: multiplied each side by 2.
  • The correct answer is: x = -80.

Thank you for your patience, and I hope this clears up the misunderstanding!