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`

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}=(30)/(60)=0.5\text{ hour}`

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

Then,
`d=4*0.5=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 =
`\frac{\text{Distance}}{\text{Speed}}=(2)/(12)=(1)/(6)\text{ hours}`

Average Speed =
`\frac{\text{Total distance}}{\text{Total time taken}}`

`=(2+2)/(0.5+(1)/(6))\\\\=(4)/((3+1)/(6))=(4*6)/(4)=6\ mph`

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