Question 125952
This type of problem is not easy. I've struggled with some.
My approach is to divide the distances that the 40 mi/hr bus
covers into 2 parts. First, how far does that bus go in 3 hrs?
I call where it is after 3 hrs the starting point. Now
the 55 mi/hr car starts and I put a stopwatch on them both
{{{d}}} = distance 55 mi/hr car covers from start to the meeting point
{{{t}}} = time for the 55 mi/hr car to cover the distance
In 3 hrs the 40 mi/hr bus covers
{{{d = 40*3}}}
{{{d = 120}}}mi
here are the equations
{{{d - 120 = 40t}}}
{{{d = 55t}}}
----------------------
{{{d = 120 + 40t}}}
Set {{{d}}} in the 1st equation = {{{d}}} in the 2nd equation
{{{120 + 40t = 55t}}}
{{{15t = 120}}}
{{{t = 8}}}hrs
So, the 55 mi/hr car has travelled for 8 hrs when they meet
{{{d = 55t}}}
{{{d = 55*8}}}
{{{d = 440}}}mi answer
I hope you can follow it and I didn't get my logic twisted
somewhere