Question

Juan jogs each day from his house to a local park, and then he jogs back along the same route. On his way to the park, he averages 4 miles per hour. On his way home, he averages 6 miles per hour. If the total trip takes mc006-1.jpg hours, which equation can be used to find x, the distance from Juan’s house to the park?

Answer 1

The equation to calculate the distance x from Juan's house to the park is 4t = 6(1 - t), where t is the time taken to jog to the park. After finding the value of t, x can be determined by substituting t into the equation.

Step-by-step explanation:

To find the equation that can be used to calculate the distance x from Juan's house to the park, we need to consider the time taken for each part of the trip. Since distance is equal to the rate multiplied by the time (d = rt), we can set up two separate equations and add them together for the total time.

On his way to the park, Juan's speed is 4 miles per hour, so let's call the time taken to go to the park t. The distance for this part of the trip would be 4t.

On his way back, his speed is 6 miles per hour. Since the total trip takes 1 hour, the remaining time for the trip back is 1 - t. The distance for this part of the trip would be 6(1 - t).

Since the distance to the park and back is the same, we can set both expressions equal to x:

• Going to the park: x = 4t
• Coming back: x = 6(1 - t)

Therefore, the equation to find x is obtained by setting both expressions for distance equal to each other:

4t = 6(1 - t)

This equation can be solved to find the value of t, and then x can be determined by substituting t into either 4t or 6(1 - t).

Answer 2

The distance traveled equals the speed v multiplied by the time t


`x = vt`:

Since the speed varies, and we only know the total time, we must rewrite this as:


`t = (x)/(v)`

If we separate this in the two 'directions', it should add up to one and a half:


`(x)/(4) + (x)/(6) = 1(1)/(2)`

That would lead me to answer b... (see same question from someone else)