Diana averages 6 mph walking to school. Averaging 35 mph on
the way back home by car, she
takes 3 hour less time.
How far is the school
from her home?

Distance between school and home = 105 miles.

Step-by-step explanation:

Let distance = D miles

Time to take walking/jogging, t1 = D/6 hours

Time by car, t2 = D/35 hours

Average time, t

= (t1+t2)/2

= D(1/6+1/35)

= (D/210)(35+6)

=41D/210 hours

Given t = t1-3 hours

41D/210 - D/6 = 3

Solve for D

41D/210 - 35D/210 = 3

(41-35)D/210 = 3

6D/210 = 3

D = 3*210/6 = 105 miles.

(Appreciate very much Diana's efforts to walk/job 105 miles to school, and we understand how lucky we are in most of Europe and North America)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is