Respuesta :
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= [tex]\frac{30}{60} = \frac{1}{2}[/tex]
We know, Distance= [tex]speed\times time[/tex]
∴ Distance of home to grocery store= [tex]4\ mph\times \frac{1}{2} \ h= 2\ miles[/tex]
Now, finding the time taken to travel back home.
Time= [tex]\frac{2}{12} = \frac{1}{6} \ h[/tex]
Next,
Total distance travel by Nadia= [tex]2\ miles+2\ miles = 4\ miles[/tex]
Total time taken travel uphil and downhill= [tex]\frac{1}{2} +\frac{1}{6}[/tex]
taking LCD
∴ Total time taken travel uphil and downhill= [tex]\frac{1\times 3+ 1\times 1}{6} = \frac{4}{6}[/tex]
Total time taken travel uphil and downhill= [tex]\frac{2}{3} \ h[/tex]
Average speed of entire trip of Nadia= [tex]\frac{4}{\frac{2}{3} }[/tex]
Multiplying the inverse.
∴ Average speed of entire trip of Nadia= [tex]4\times \frac{3}{2} = 2\times 3[/tex]
Hence, Average speed of entire trip of Nadia is 6mph.
