Question 44395
{{{d[1]}}} = distance travelled by first cyclist
{{{d[2]}}} = distance travelled by second cyclist
{{{v[1]}}} = speed of first cyclist   = 6 mph
{{{v[2]}}} = speed of second cyclist  = 10 mph
{{{t[1]}}} = time first cyclist has been travelling 
{{{t[2]}}} = time second cyclist has been travelling


We know that speed is eqaul to distance divided by time: {{{v=d/t}}}
so {{{d[1]=v[1]*t[1]}}} and {{{d[2]=v[2]*t[2]}}}.
We also know that when the second cyclist starts, the first has been travelling for three hours, so {{{t[1]=t[2]+3}}}
When the second cyclist catches up with th first, the distance travelled by each cyclist is the same: {{{d[1]=d[2]}}}.
We are looking to find {{{t[2]}}}.

From the working, we can deduce:
{{{v[1]*(t[2]+3)=v[2]*t[2]}}}
{{{6*(t[2]+3)=10*t[2]}}}
{{{6*t[2]+18=10*t[2]}}}
{{{18=4t[2]}}}
{{{t[2]=18/4}}}
{{{t[2]=4.5}}}

So 4.5 hours will pass before the second cyclist catches up with the first from the time when the second cyclist started biking.



I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk