Question 323655
You need 2 equations since there are 2 cars.
Let {{{d}}} = the distance in miles the 80 mi/hr car has to go to catch
the 60 mi/hr car
Then {{{d - 1}}} = the distance the 60 mi/hr car goes until it is caught by
the 80 mi/hr car
They both will travel for he same amount of time - call it {{{t}}}
Ist car:
{{{d = r*t}}}
{{{d = 80t}}}
2nd car:
{{{d - 1 = 60t}}}
{{{d = 60t + 1}}}
Then, by substitution:
{{{80t = 60t + 1}}}
{{{20t = 1}}}
{{{t = 1/20}}} hrs
{{{1/20}}} hrs x {{{60}}} min/hr = 3 min
The 80 mi/hr car takes 3 min to catch the 60 mi/hr car
check:
{{{d = 80t}}}
{{{d = 80*(1/20)}}}
{{{d = 4}}} mi
and
{{{d = 60t + 1}}}
{{{d = 60*(1/20) + 1}}}
{{{d = 3 + 1}}}
{{{d = 4}}} mi
OK