How to solve this word problem help

Ramona cycles from her house to school at 15 miles per hour. Upon arriving, she immediately cycles home at 25 miles per hour. If the entire round-trip takes her 32 minutes, then what is the average speed, in miles per hour for the entire trip?

We know that the distance from the school to the house is the same as the distance from the house to the school which gives us the equation:
x*15=y*25
where x and y are the time for the trips in either direction.
And the total time is 32 minutes so we also have:
x+y=32
Isolating x in the first equation gives us x=25/15y=5/3y and inserting this in the second equation gives us: 32=x+y=(5/3)y+y=(8/3)y so y=32*3/8=12. No we can insert again in the second equation to get x=32-12=20. Now we can calculate the average speed:
v=(15*20+25*12)/32=18.75 m/h

va = ( v + v0 ) / 2
va = average velocity
v0 = initial velocity
v = final velocity

va = 24306000 ft/s
v = 47820000 ft/s
v0 = 792000 ft/s
1 foot/seconds = 5.26094276 × 10^-8 miles/hour=0.00000001x5.26094276=n

assuming the distance from home to school is D
going to school took her D/15 and back home took her D/25 hours
average speed is 2D/(D/15+D/25) = 2/(1/15+1/25) = 150/ (3+5) = 18.75 mph

Let the distance be x miles

x / 15 + x /25 = 32/60 = 8/15

MULTIPLY BY 75

5x + 3x = 40

8x = 40

x = 5 miles

Average speed = distance / time = 10 / 32/60 = 600 /32 = 150 /8 = 18.75 mph ANSWER

CHECK
18.75 X 32/60 = 10miles