Starting at home, Nadia traveled uphill to the grocery store for 30 minutes at just 4 mph. 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?

Answer: [tex]6\ mph[/tex]Step-by-step explanation:Let d be the distance from Nadia's home to the grocery store.Given : Nadia traveled uphill to the grocery store for 30 minutes at just 4 mph.∵ 1 hour = 60 minutes.Then, [tex]30\text{ minutes}=\dfrac{30}{60}=0.5\text{ hour}[/tex]Since [tex]\text{Distance = Speed * Time}[/tex]Then,  [tex]d=4\times0.5=2\text{ miles}[/tex] Also, She then traveled back home along the same path downhill at a speed of 12 mph.Then, Time taken to travel back home = [tex]\dfrac{\text{Distance}}{\text{Speed}}=\dfrac{2}{12}=\dfrac{1}{6}\text{ hours}[/tex]Average Speed =[tex]\dfrac{\text{Total distance}}{\text{Total time taken}}[/tex][tex]=\dfrac{2+2}{0.5+\dfrac{1}{6}}\\\\=\dfrac{4}{\dfrac{3+1}{6}}=\dfrac{4\times6}{4}=6\ mph[/tex]Hence, her average speed for the entire trip from home to the grocery store and back = [tex]6\ mph[/tex]