Estimating hiking speed...

[Billy]

You go on an 18 mile hike.
The first half of the hike, you hike 3 miles per hour.
The second half of the hike, you hike 1 mile per hour.

The average of three and one is two.
So, your average hiking speed for the whole hike is 2 miles per hour.

Right?

Math is easy.

 

[ow2010]

By first/second half of the hike, do you mean time spent hiking or mileage? Because if you mean mileage (as I assumed) this means it was a 12 hour hike...
18 miles divided by 12 hours equals 1.5 mph...factor in stationary time (lunch, other breaks) and 2 mph is probably correct.

Not sure if there was an underlying joke here tho

 

[sierra]

You should quit hiking and go cure cancer.

 

[nartreb]

On the other hand if "half the hike" refers to time, then yes, you can average those two speeds and get the correct average speed for the hike.

speed = distance in miles over time in hours.

T = total hiking time in hours.

half the hike = T/2.

3 mph * T/2 + 1 mph * T/2 = 18 mi
Now multiply both sides by two hours (and divide both sides by 1 mile, to cancel the miles unit):
3T + 1T = 36 hours
T = 36/4 = 9 hours

Check:
9 hours * 2mph = 18 miles. Check.

More generally, to do math on rates (or any fraction) you always want to pay attention to the denominator (time in this case).

 

[DougPaul]

We should note that the definition of average hiking speed is:

avg_speed = total_distance / total_time

Doug

 

[grog]

trick ?

To get correct answer Billy must specify whether its time or distance when referring to half of hike, two different answers. Trick question?

Whenever I go on trip, miles is most important.

grog