Question 9734
For the walker:

{{{d1 = r1*t1}}} r1 = 4 mph
{{{d1 = 4*t1}}} t1 = t2 + 2/3 hrs.  (40 mins = 2/3 hrs)

For the cyclist:

{{{d2 = r2*t2}}} r2 = 16 mph 
{{{d2 = 16*t2}}}
{{{d1 = 4(t2+2/3)}}}

When they meet, d1 = d2.

{{{4(t2+2/3) = 16*t2}}} Simplify and solve for t2

{{{4*t2 + 8/3 = 16*t2}}} Subtract 4*t2 from both sides.

{{{8/3 = 12*t2}}} Divide both sides by 12.

{{{8/36 = t2}}}

t2 = 2/9 hours They will meet 2/9 hrs (13.3... mins) after the cyclist starts.

They will have traveled a distance of d1 = 16*t2 or 16 mph(2/9 hrs) = 3.56 miles.

Has the walker completed the course?  Who knows!  How long is the course?

Check:

{{{d1 = 4 mph(t1)}}}
{{{d1 = 4 mph(t2+2/3)}}}
{{{d1 = 4(2/9 + 2/3)}}}
{{{d1 = 4(2/9 + 6/9)}}}
{{{d1 = 4(8/9)}}}
{{{d1 = 32/9}}} miles.

{{{d2 = 16 mph(t2)}}}
{{{d2 = 16 mph(2/9 hrs)}}}
{{{d2 = 32/9}}} miles.