In the first 120 miles over 240 mile journey a truck driver maintained an average speed of 50 mph what was his average featuring the next 120 miles if the average speed of the entire trip with 60 mph

The average speed over the entire trip was 60 mph, which must equal the distance traveled (240 miles) times the elapsed time.  Dividing  60 mph into 240 miles gives us the elapsed time:  (240 miles) / (60 mph) = 4 hours total.

Next:  determine the length of time required to drive the first 120 miles at 50 mph.  It is (120 miles) / (50 mph), or 2.4 hours.

Next, find the length of time required to drive the second 120 miles.  It is 4 hours less 2.4 hours, or 1.6 hours.

Lastly, find the average speed over which the second 120 miles were covered in 1.6 hours:

average speed (2nd 120 miles) = (120 miles) / (1.6 hours) = 75 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.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

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

the table tells us

g(-2) = 1g(1) = 31

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).

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