Question 311401
Let the distance to school be x miles

speed to school = 15 mph
time taken to go to school = x/15
..
Similarly time to return from school = x/23

Total time taken = 32 minutes.= 32/60 hours
x/15 + x/23 = 32/60

23x+15x / 15*23 = 32/60
38x = 32*15*23 /60
38x=184
x= 4.84 miles

UP & down she travels 2*4.84 miles = 9.68

Total time taken = 32/60 hours

Average speed = 9.68 /  32/60
9.68 * 60 /32

18.15 mph