Nathan is meeting his friend Tim at the Crown Valley Dog Park. Nathan lives 2 miles from the park, and Tim lives 4 miles from the park. They leave for the park at the same time, but Nathan and his dog walk at 3 miles per hour, while Tim and his dog jog at 7 miles per hour. Which equation can you use to find h, the number of hours it will take for Nathan and Tim to be the same distance from the park? Choices: (A)2h - 3 = 4h - 7 (B)2 - 3h = 4 - 7h How long will it take for Nathan and Tim to be the same distance from the park? Simplify any fractions. ____ hours

Question

Nathan is meeting his friend Tim at the Crown Valley Dog Park. Nathan lives 2 miles from the park, and Tim lives 4 miles from the park. They leave for the park at the same time, but Nathan and his dog walk at 3 miles per hour, while Tim and his dog jog at 7 miles per hour. Which equation can you use to find h, the number of hours it will take for Nathan and Tim to be the same distance from the park?   Choices: (A)2h - 3 = 4h - 7 (B)2 - 3h = 4 - 7h  How long will it take for Nathan and Tim to be the same distance from the park? Simplify any fractions.   ____ hours

Bytelearn · Accepted Answer

Set Up Equation: To find the equation that represents the situation, we need to set up an equation where the distances that Nathan and Tim have traveled from their respective starting points are equal. Since they start at different distances from the park and travel at different speeds, we will use the formula distance = speed × time.Nathan's Distance: Nathan starts 2 miles from the park and walks at 3 miles per hour. The distance Nathan will have covered after h hours is 3h miles.Tim's Distance: Tim starts 4 miles from the park and jogs at 7 miles per hour. The distance Tim will have covered after h hours is 7h miles.Remaining Distances: Since they want to be the same distance from the park, we need to subtract the distance they have traveled from their starting distances. For Nathan, it will be 2 - 3h miles from the park, and for Tim, it will be 4 - 7h miles from the park.Set Equal: To find when they are the same distance from the park, we set the expressions for their remaining distances equal to each other: 2 - 3h = 4 - 7h.Combine Terms: Now we solve for h. First, we add 7h to both sides of the equation to get all the h terms on one side: 2 - 3h + 7h = 4 - 7h + 7h.Isolate h Term: Simplifying the equation, we get 2 + 4h = 4.Solve for h: Next, we subtract 2 from both sides to isolate the term with h: 2 + 4h - 2 = 4 - 2.Final Result: This simplifies to 4h = 2.Finally, we divide both sides by 4 to solve for h: h = 2/4.Simplifying the fraction, we get h = 1/2.

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