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= 
We know, Distance= 
∴ Distance of home to grocery store= 
Now, finding the time taken to travel back home.
Time= 
Next,
Total distance travel by Nadia= 
Total time taken travel uphil and downhill= 
taking LCD
∴ Total time taken travel uphil and downhill= 
Total time taken travel uphil and downhill= 
Average speed of entire trip of Nadia= 
Multiplying the inverse.
∴ Average speed of entire trip of Nadia= 
Hence, Average speed of entire trip of Nadia is 6mph.