Question 282750
You want to overuse this formula:

{{{D = R * T}}}

We are looking for time, the trick in this problem is the boy on the bike begins to overtake his brother, they will have equal distances.

Guy walking:

{{{D = 3(t+1/6)}}} because he started 10 minutes early, that is 1/6 an hour.


Guy Bike:
{{{D = 6(t)}}}

Since the distances are equal:

{{{3(t+1/6) = 6t}}}
{{{3t + 1/2 = 6t}}} distributive property
{{{3t = 1/2}}} subtract 3t on both sides:
{{{t = 1/6}}}

It will take 1/6th an hour (10 minutes) to catch up!