Two friends live 3 miles apart along the same road. If they walk toward each other at rates that differ by half mile per hour and meet 24 minutes later, how fast is each person walking

their speeds are 3.5mph and 4 mph

Step-by-step explanation:

Since both friends live 3 miles apart along the same road, by the time they meet, they would have covered 3 miles.

Let x represent the speed of the slower friend.

If differ by half mile per hour, it means that the speed of the faster friend is (x + 0.5) mph

They meet after 24 minutes(24/60 = 0.4 hours)

Distance = speed × time

Distance covered by the slower friend in 0.4 hours is

x × 0.4 = 0.4x

Distance covered by the faster friend in 0.4 hours is

0.4(x + 0.5) = 0.4x + 0.2

Since the total distance is 3 miles, then

0.4x + 0.4x + 0.2 = 3

0.8x = 3 - 0.2 = 2.8

x = 2.8/0.8

x = 3.5 mph

The speed of the faster friend is

3.5 + 0.5 = 4 mph

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0