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)2 - 3h = 4 - 7h (B)2h - 3 = 4h - 7 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)2 - 3h = 4 - 7h (B)2h - 3 = 4h - 7  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 Equations: To find the equation that represents the situation, we need to set up an equation that shows when Nathan and Tim will be the same distance from the park. We know that distance equals rate times time, so we can set up the following equations for Nathan and Tim:  For Nathan: Distance remaining = Initial distance - (Rate * Time) For Tim: Distance remaining = Initial distance - (Rate * Time)  Since we are looking for when they are the same distance from the park, we can set these two expressions equal to each other.Equation for Distance: Nathan's distance from the park after h hours: 2 - 3h Tim's distance from the park after h hours: 4 - 7h  Setting these equal to each other gives us the equation: 2 - 3h = 4 - 7hSolve Equation: Now we need to solve the equation 2 - 3h = 4 - 7h to find the value of h, which represents the number of hours it will take for Nathan and Tim to be the same distance from the park.  First, we can add 7h to both sides of the equation to get all the h terms on one side: 2 - 3h + 7h = 4 - 7h + 7h 2 + 4h = 4Add and Subtract: Next, we subtract 2 from both sides of the equation to isolate the term with h: 2 + 4h - 2 = 4 - 2 4h = 2Divide to Find h: Finally, we divide both sides of the equation by 4 to solve for h: 4h / 4 = 2 / 4 h = 1/2

Full solution

More problems from Solve linear equations with variables on both sides: word problems

Related topics