Diana averages 6 mph walking to school. Averaging 35 mph on
the way back home by car, she
takes hour less time.
4
How far is the school
from her home?
[?] miles
Round to the nearest hundredth.

9514 1404 393

  7.24 miles

Step-by-step explanation:

The relationship between time, speed, and distance is ...

  time = distance/speed

For distance d in miles, her time in hours walking to school is d/6. Her time traveling home is d/35. The difference of these is 1 hour:

  d/6 -d/35 = 1

  d(1/6 -1/35) = 1

  d(35 -6)/(35·6) = 1

  d = 35·6/29 ≈ 7 7/29 ≈ 7.2414 . . . . miles

The school is about 7.24 miles from Diana's home.

Additional comment

Diana is quite the athlete. World-class race-walking speeds are on the order of 8 miles per hour. Casual walking speeds are on the order of 3 miles per hour.