Starting at home, luis traveled uphill to the hardware store for 30 minutes st just 8mph. he then traveled back home along the same path downhill at a speed of 24 mph. what is his average speed for the entire trip from home to the hardware store and back?

1.

The main formula we use is:

Distance traveled = average Speed * Time,

in short: D = S * T

2.

" luis traveled uphill to the hardware store for 30 minutes at speed 8mph. "

we have the speed and the time = 30 min = 1/2 h

so we can find distance:

D=ST=8 (mi/h) * 1/2 (h) = 4 mi

3.

Now we have D, and the speed 24 mph, so we can find the time it takes Luis to travel back home:

D=S*T

T = D/S = 4 (mi) / 24 (mi/h) = 1/6 h

4.

The total distance is D+D = 4 + 4 = 8 (mi)

the total time is 1/2 + 1/6 = 3/6 + 1/6 = 4/6 = 2/3 (h)

So we can find the average speed of the entire trip is:

S=8 / (2/3) = 8 * (3/2) = 4*3=12 (mph)

Answer : 12 mph