Question 133407
Distance = speed * time

{{{280 = S * t }}}
{{{ 280/S = t }}}

If the car was drive 5 mph faster, it would have arrived 1 hour earlier. So 
{{{280 = (S+5) * (t-1)}}}
{{{280 = (S+5) * ((280/S) -1) }}}
{{{ 280 = (S+5) * ((280 -S)/S) }}}
{{{ 280 = (280 - S) + (5(280 -S))/S }}}
{{{ 0 = -S + (1400 -5S)/S }}}
{{{ 0 = -S^2 -5S + 1400 }}}
{{{ 0 = S^2 + 5S - 1400 }}}
{{{ 0 = (S + 40) (S  - 35) }}}
S = -40 or S = 35. Since S can't be negative, S must be 35.

Check your answer.
280 / 35 = 8 hours
289 / 40 = 7 hours. Check!