Answer:
6 mph
Step-by-step explanation:
Here is the complete question: Starting at home Nadia traveled uphill to the grocery store for 30 minutes at just 4mph. She then traveled back home along the same path downhill at a speed of 12 mph. What is her average speed for the entire trip from home to the grocery store and back?
Given: Time taken to travel uphill to the grocery store is 30 minutes.
Speed of travelling uphill to the grocery store is 4 mph.
Speed of travelling downhil to the home is 12mph.
First converting the unit if time given:
Time taken to travel uphill to the grocery store= ![\frac{30}{60} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B60%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
We know, Distance= ![speed\times time](https://tex.z-dn.net/?f=speed%5Ctimes%20time)
∴ Distance of home to grocery store= ![4\ mph\times \frac{1}{2} \ h= 2\ miles](https://tex.z-dn.net/?f=4%5C%20mph%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%5C%20h%3D%202%5C%20miles)
Now, finding the time taken to travel back home.
Time= ![\frac{2}{12} = \frac{1}{6} \ h](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B12%7D%20%3D%20%5Cfrac%7B1%7D%7B6%7D%20%5C%20h)
Next,
Total distance travel by Nadia= ![2\ miles+2\ miles = 4\ miles](https://tex.z-dn.net/?f=2%5C%20miles%2B2%5C%20miles%20%3D%204%5C%20miles)
Total time taken travel uphil and downhill= ![\frac{1}{2} +\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%2B%5Cfrac%7B1%7D%7B6%7D)
taking LCD
∴ Total time taken travel uphil and downhill= ![\frac{1\times 3+ 1\times 1}{6} = \frac{4}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%5Ctimes%203%2B%201%5Ctimes%201%7D%7B6%7D%20%3D%20%5Cfrac%7B4%7D%7B6%7D)
Total time taken travel uphil and downhill= ![\frac{2}{3} \ h](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20%5C%20h)
Average speed of entire trip of Nadia= ![\frac{4}{\frac{2}{3} }](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B%5Cfrac%7B2%7D%7B3%7D%20%7D)
Multiplying the inverse.
∴ Average speed of entire trip of Nadia= ![4\times \frac{3}{2} = 2\times 3](https://tex.z-dn.net/?f=4%5Ctimes%20%5Cfrac%7B3%7D%7B2%7D%20%3D%202%5Ctimes%203)
Hence, Average speed of entire trip of Nadia is 6mph.