Question

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 1

Answer: $6\ mph$

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, $30\text{ minutes}=\dfrac{30}{60}=0.5\text{ hour}$

Since $\text{Distance = Speed * Time}$

Then,  $d=4\times0.5=2\text{ miles}$

Also, She then traveled back home along the same path downhill at a speed of 12 mph.

Then, Time taken to travel back home = $\dfrac{\text{Distance}}{\text{Speed}}=\dfrac{2}{12}=\dfrac{1}{6}\text{ hours}$

Average Speed =$\dfrac{\text{Total distance}}{\text{Total time taken}}$

$=\dfrac{2+2}{0.5+\dfrac{1}{6}}\\\\=\dfrac{4}{\dfrac{3+1}{6}}=\dfrac{4\times6}{4}=6\ mph$

Hence, her average speed for the entire trip from home to the grocery store and back = $6\ mph$