(baby math) rates and average speed

Question

I'm sorry for this low level question, since i would really like to become a data scientist i study everyday math from the very beginning, i learn through khan academy and everything was fine since i started until this question i can't really well visualize

rates, distance problem

Of course they give the answer at Khan Academy but i can't visualize at all, so i would like to know if anyone can explain me the answer by himself so maybe i would understand it better than by the video

Thank you.

Answer 1

The distance to the store is $8\times0.75=6$ miles. Therefore, the total distance travelled is $12$ miles. The time the journey back takes is $6/24=0.25$ hours (i.e. $15$ minutes).

The average speed is $$\frac{\text{distance}}{\text{time}}=\frac{12}{0.75+0.25}=\frac{12}{1}=12 \text{ mph}.$$

Answer 2

Vizualization almost without words : Consider speeds as slopes of the different line segments, that add like vectors (I don't know if you have already covered these subjects); of course, you need some basic calculations like those done by @woofy and @callculus.