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 1 and one-half hours, which equation can be used to find x, the distance in miles from Juan's house to the park? Distance (mi) Rate (mi/hr) Time (hr) Trip to Park x 4 mph Trip to Home x 6 mph StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1 StartFraction x Over 4 EndFraction + StartFraction x Over 6 EndFraction = 1 and one-half 4 x + 6 x = 1 and one-half 4 x + 6 x = 1

Answer 1

Answer:

$\frac{x}{4}+ \frac{x}{6}=1\frac{1}{2}$

Step-by-step explanation:

Speed is the ratio of distance traveled to the total time taken. It is given by the equation:

speed = distance / time.

Given that the distance to the park = x miles.

On his way to the park, he averages 4 miles per hour. Let the time taken be $t_1$ therefore:

speed = distance / time.

4 = x /  $t_1$

$t_1$ = x / 4

On his way home, he averages 6 miles per hour Let the time taken be $t_2$ therefore:

speed = distance / time.

6 = x /  $t_2$

$t_2$ = x / 6

The total trip takes 1 and one-half hours, therefore:

$t_1+t_2=1\frac{1}{2}\\\\ substituting\ t_1 \ and\ t_2:\\\\\frac{x}{4}+ \frac{x}{6}=1\frac{1}{2}$