Question 162015
{{{d = r*t}}}
Given:
{{{d = 240}}}km
If the speed was {{{r + 8}}} km/hr
the time would have been {{{t - 1}}}hr
The equations are:
{{{240 = r*t}}} and
{{{240 = (r + 8)*(t - 1)}}}
{{{240 = rt + 8t - r - 8}}}
And, since {{{240 = r*t}}},
{{{240 = 240 + 8t - r - 8}}}
Subtract {{{240}}} from both sides
{{{0 = 8t - r - 8}}}
{{{r = 8*(t - 1)}}}
Substitute this in {{{240 = r*t}}}
{{{240 = 8*(t - 1)*t}}}
{{{240 = 8t^2 - 8t}}}
Divide both sides by {{{8}}}
{{{t^2 - t - 30 = 0}}}
{{{(t - 6)(t + 5) = 0}}}
{{{t = -5}}} 
{{{t = 6}}} hrs
{{{240 = r*t}}}
{{{r = 240 / t}}}
{{{r = 240/6}}}
{{{r = 40}}} km/hr
The speed of the train was 40 km/hr
check answer:
{{{240 = r*t}}}
{{{240 = (r + 8)*(t - 1)}}}
{{{240 = (40 + 8)*(6 - 1)}}}
{{{240 = 48*5}}}
{{{240 = 240}}}
OK