Question 213740
If the car drives 40 mi/hr or less, it can  never
catch the bus.
The car leaves 1 hr after the bus has left
In 1 hr, the bus has gone 
{{{d =40*1}}}
{{{d = 40}}} mi
I have a stopwatch which I will start when the car leaves
and I'll stop it when the car catches the bus.
Both vehicles will drive for 2 hrs, but the bus has
a {{{40}}} mi headstart.
Let {{{d}}} = distance the car goes in 2 hrs
Let {{{r}}} = speed of the car in mi/hr
{{{d - 40}}} = distance the bus travels
Let {{{t = 2}}} hrs for both
For car:
(1) {{{d = r*2}}}
For bus:
(2) {{{d - 40 = 40*2}}}
Substitute (1) in (2)
{{{2r - 40 = 80}}}
{{{2r = 120}}}
{{{r = 60}}}
The car needs to go 60 mi/hr to catch the bus in 2 hrs
check answer
In 2 hrs, the bus goes
{{{d = 40*2}}}
{{{d = 80 mi}}}
{{{80 + 40 = 120}}}
The car needs to go a total of 120 mi in 2 hrs
{{{d = r*t}}}
{{{120 = r*2}}}
{{{r = 60}}} mi/hr
OK