# Math Help - Mean speed

1. ## Mean speed

I walk 1km up the hill at 4km/h and 1km down the hill at 6km/h.

What is my mean speed?

2. Originally Posted by Natasha1
I walk 1km up the hill at 4km/h and 1km down the hill at 6km/h.

What is my mean speed?
Average speed (ie mean speed) is defined as "total distance travelled" divided by "time to travel the distance." (It is a common error to find two speeds and take a geometric average.) We know the distance, we need to find the time.

$t_1 = \frac{x_1}{v_1}=\frac{1 \, km}{4 \, km/hr}=\frac{1}{4} \, hr$

$t_2 = \frac{x_2}{v_2}=\frac{1 \, km}{6 \, km/hr}=\frac{1}{6} \, hr$

$t = t_1+t_2 = \frac{1}{4} \, hr+\frac{1}{6} \, hr =\frac{5}{12} \, hr \approx 0.416667 \, hr$

So the average speed for the round trip will be:
$v = \frac{x}{t}=\frac{2 \, km}{0.416667 \, hr}=4.8 \, km/hr$

-Dan