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

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

:

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

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

That would lead me to answer b

Step-by-step explanation:

have a nice day :)

step-by-step explanation:

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft