Speed, time, distance - there's some great equations to be had here, but for moving on foot, there are a few simple ways to deal with this.
Over the next two puzzles we'll look at the time it takes to cover distances over the ground. And to begin with we'll use some 'rules'. This week we'll use Naismith's rule and next week we'll have a look at a couple of corrections (slope, age and fitness) to cover some other scenarios.
Naismith's rule; random facts first - suggested first in 1892, and was used in UK Law in 1996 and 2004 revisions (Adventurous Activities Licensing Regulations) to calculate when someone would be more than 30 minutes away from a road or place of refuge.
In modern speak (it was originally written in Miles distance and feet of ascent, but now most UK maps are metric, it's far more useful to do Kilometres and metres) it works on the time taken to cover a certain distance when walking - so the first assumption is that an average person walks at 5km/h (or 1 km every 12 mins) and the second assumption is that we add 1 minute for each 10m of height gained.
These two things are great on a map where the grid squares are 1 km, and the contour intervals are 10m. Have a look at some of the earlier puzzles if you want to see these described in a bit more detail.
So, on this map, to go from A-B along the trail (1 km) would take 12 minutes, because we aren't climbing any contours.
Where as the A-B route up Braich, which is also 1 km long would, using the rule take 12 minutes for the km, plus 9 minutes for crossing 9 contour lines (i.e. climbing up 90m) this giving a 21 minutes in total.
Using Naismith's rule then, how long would it take to do the following journeys, on foot
From SH 7134 3066 to SH 7104 3452 along the A470
From SH 6301 3009 to SH 6457 2987 along the public footpath
In more open country, it can take a bit of time to work out, so try -
From the wall crossing at SH 8151 3809, follow the wall east, climbing up the spur on Craig y Hyrddod before continuing along the field boundary curving south and then west to the summit of Arenig Fawr and trig point at SH 8270 3694
You can get the workings for the answers here