A motorist travels 90 miles at a rate of 20 miles per hour. If he returns the same distance at a rate of 40 miles per hour, what is the average speed for the entire trip, in miles per hour? (Pls explain throughly with your answer)

Step-by-step explanation:

We can use the formula (distance  = rate * time) to solve this problem.

If the motorist is travelling 90 miles to and back on a trip, he has travelled miles total. This represents in our formula.

Now we need to find the total time.

On the first trip, it's given that the motorist travels at a rate of 20 mph. Therefore, the time this trip took to travel 90 miles is:

hours

On the second trip back, he travels the same distance (90 miles) at a rate of 40 mph. Therefore, the time the trip took is:

hours

Therefore, the total time is hours.

Now can calculate the average speed of the entire trip:

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb