Question

Starting at home, Luis traveled uphill to the gift store for 50 minutes at just 6 mph. He then traveled back home along the same path downhill at a speed of 12 mph.
What is his average speed for the entire trip from home to the gift store and back?

Answer 1

Average speed for the entire trip, both ways, is

                 (Total distance) divided by (total time) .

We don't know the distance from his house to the gift store,
and we don't know how long it took him to get back.
We'll need to calculate these.

-- On the trip TO the store, it took him 50 minutes, at 6 mph.
-- 50 minutes is 5/6 of an hour.
-- Traveling at 6 mph for 5/6 of an hour, he covered 5 miles.
-- The gift store is 5 miles from his house.
-- The total trip both ways was 10 miles.

-- On the way BACK home from the store, he moved at 12 mph.
-- Going 5 miles at 12 mph, it takes  (5/12 hour) = 25 minutes.

Now we have everything we need.

Distance:
         Going:       5 miles
         Returning:  5 miles
         Total         10 miles

Time:
         Going:        50 minutes
         Returning:   25 minutes
         Total:          75 minutes  =  1.25 hours  

         Average speed for the whole trip =

                       (total distance) / (total time)

                   =      (10 miles)  /  (1.25 hours)

                   =       (10 / 1.25)  miles/hours 

                   =          8 miles per hour