A Tangled Tale
S. McAdams, S. Pinion, & L. Stueve
A problem taken from Lewis Carroll.
A man walked for 5 hours. First along level road, then up a hill.
Assuming he began and ended his walk at the same spot, and that he walked
at 4 mph on level ground, 3 mph up hill, and 6 mph down hill. Find the distance
that he walked.
Assign D1 = 3 mph up hill, D2 = 6 mph down hill, and D3 = 4 mph on level
ground. We know that {D1 / 3 mph + D2 / 6 mph + D3 / 4 mph = 5 hours}. We
can also say that D1 = D2 since you travel the same dist`nce up hill as
down if you begin and end in the same place.
So, now we have {(D1 /
3 mph + D1 / 6 mph )+ D3/ 4 mph = 5 hours} or
{3D1 / 6 mph + D3 / 4 mph = 5 hours}. Clearing the fractions we have
{2D1 + D3 = 20} and since D1 = D2 we find D1 + D2 + D3 = 20 miles
So our gentleman friend's constitutional of 5 hours covered
~20miles!! What a hike!!