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?

Let S = his average speed.

Let D = distance traveled one way

Time = distance / speed

Set up an equation:

d/6 + d/12 = 2d/S

Multiply the equation by 12s:

12s(d/6) + 12s(d/12) = 12s(2d/s)

Simplify to get:

2sd + sd = 24d

Combine like terms:

3sd = 24d

Divide both sides by d:

3s = 24

Divide both sides by 3:

s = 24/3

s = 8

His average speed was 8 mph.