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

Answer 1

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= $\frac{30}{60} = \frac{1}{2}$

We know, Distance= $speed\times time$

∴ Distance of home to grocery store= $4\ mph\times \frac{1}{2} \ h= 2\ miles$

Now, finding the time taken to travel back home.

Time= $\frac{2}{12} = \frac{1}{6} \ h$

Next,

Total distance travel by Nadia= $2\ miles+2\ miles = 4\ miles$

Total time taken travel uphil and downhill= $\frac{1}{2} +\frac{1}{6}$

taking LCD

∴ Total time taken travel uphil and downhill= $\frac{1\times 3+ 1\times 1}{6} = \frac{4}{6}$

Total time taken travel uphil and downhill= $\frac{2}{3} \ h$

Average speed of entire trip of Nadia= $\frac{4}{\frac{2}{3} }$

Multiplying the inverse.

∴ Average speed of entire trip of Nadia= $4\times \frac{3}{2} = 2\times 3$

Hence, Average speed of entire trip of Nadia is 6mph.