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? How long will it take for Nathan and Tim to be the same distance from the park? Simplify any fractions.

1) h = (4 - 2) / (7 - 3)
2) h = (2 - 4) / (3 - 7)
3) h = (4 - 2) / (3 - 7)
4) h = (2 - 4) / (7 - 3)

Answer 1

Nathan and Tim will be the same distance from the park after 1/5 of an hour, or 12 minutes. The correct equation to represent this scenario is (2 + 3h) = (4 - 7h), which was not listed among the options provided.

Step-by-step explanation:

We need to find the time h when Nathan and Tim will be the same distance from the park. Since they are both moving towards the park and they started at the same time, we can set up an equation where the distances that Nathan and Tim have traveled, when added to the remaining distances to the park, are equal.

Nathan's distance covered in hours h will be 3h (since he walks at 3 miles per hour). Tim's distance covered will be 7h (since he jogs at 7 miles per hour).

To be the same distance from the park, we can set up the equation: Nathan's starting distance - Nathan's distance traveled = Tim's starting distance - Tim's distance traveled. Therefore, the equation is (2 - 3h = 4 - 7h).

To solve for h, we rearrange the terms: 3h - 7h = 4 - 2, which simplifies to -4h = 2. Dividing both sides by -4 gives us h = -1/2. However, time cannot be negative, so we have likely made an error. Instead, we should compare the distances each person has to travel with the speed they are traveling, which brings us back to our original equation, arranging it correctly: (2 + 3h = 4 - 7h). Solving for h from this equation gives us 3h + 7h = 4 - 2, which simplifies to 10h = 2. Dividing both sides by 10 gives us h = 2/10 or h = 1/5. Therefore, it will take Nathan and Tim 1/5 of an hour, or 12 minutes, to be the same distance from the park.

The correct option from the provided choices is the one that represents the correct setup of the equation factoring in the distances yet to travel towards the park and their speeds: (2 + 3h) = (4 - 7h), which is actually none of the given options.