Question 199978
Mike can run the mile in 6 minutes and Dan can run the mile in 9 minutes.
If Mike gives Dan a head-start of 1 minute, how far from the start will Mike pass Dan? 
How long does it take?
:
Let t = M's running time
then
(t+1) = D's running time
:
When M catches D, they will have run the same distance
Write a distance equation from this fact
{{{1/6}}}t = {{{1/9}}}(t+1)
Multiply both side by 18
3t = 2(t+1)
3t = 2t + 2
3t - 2t = 2
t = 2 minutes for M to catch D
:
Dist:
{{{1/6}}} * 2 = {{{1/3}}} mile
and
{{{1/9}}} * 3 = {{{1/3}}} mile