Question 1205546

On a recent trip, a trucker traveled {{{525}}} mi at a constant rate. 

{{{d=rt}}}

t=d/r

{{{t=525/r}}}

Because of road conditions, the trucker then reduced the speed by {{{30}}} mph.

{{{(r-30)}}}

An additional {{{45}}} mi was traveled at the reduced rate.

{{{t=45/(r-30)}}}

 The entire trip took {{{8}}} h. 

{{{8=525/r+45/(r-30)}}}

{{{8(r-30)=525(r-30)/r+45}}}

{{{8r-240=(525 r - 15750)/r+45}}}...multiply by {{{r}}}

{{{8r^2-240r=525 r - 15750+45r}}}

{{{8r^2-240r-525 r +15750-45r=0}}}

{{{8 r^2 - 810 r + 15750=0}}}

{{{2 (r - 75) (4 r - 105) = 0}}}


{{{r=75 }}}
or 
{{{r=105/4=26.25}}}....disregard because speed was reduced by {{{30mph}}}


so, the rate of the trucker for the first {{{525}}} mil was {{{75mph}}}