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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

User Mike Braun
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1 Answer

3 votes

Answer:

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.

User Erik Pilz
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7.8k points