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

6 mph

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=
`(30)/(60) = (1)/(2)`

We know, Distance=
`speed* time`

∴ Distance of home to grocery store=
`4\ mph* (1)/(2) \ h= 2\ miles`

Now, finding the time taken to travel back home.

Time=
`(2)/(12) = (1)/(6) \ h`

Next,

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

Total time taken travel uphil and downhill=
`(1)/(2) +(1)/(6)`

taking LCD

∴ Total time taken travel uphil and downhill=
`(1* 3+ 1* 1)/(6) = (4)/(6)`

Total time taken travel uphil and downhill=
`(2)/(3) \ h`

Average speed of entire trip of Nadia=
`(4)/((2)/(3) )`

Multiplying the inverse.

∴ Average speed of entire trip of Nadia=
`4* (3)/(2) = 2* 3`

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