<PRE><B>Question 1129074</B>
&lt;br&gt;
Let the distances (km) for the two parts of the trip be x and 400-x.  Then&lt;br&gt;
The total number of hours for the trip, at 100km/hr for the first part and 80km/hr for the second, was&lt;br&gt;
{{{x/100+(400-x)/80}}}&lt;br&gt;
If the two speeds had been switched, the total number of hours would have been&lt;br&gt;
{{{x/80+(400-x)/100}}}&lt;br&gt;
The second trip would have taken 0.5 hours longer:&lt;br&gt;
{{{x/80+(400-x)/100 = x/100+(400-x)/80+0.5}}}&lt;br&gt;
Multiply through by the LCM, 400:&lt;br&gt;
{{{5x+4(400-x) = 4x+5(400-x)+200}}}&lt;br&gt;
Solve....&lt;br&gt;
{{{5x+1600-4x = 4x+2000-5x+200}}}
{{{2x = 600}}}
{{{x = 300}}}&lt;br&gt;
He traveled at 100km/hr for 300 km (3 hours) and at 80 km/hr for 100 km (1.25 hours); total time 4.25 hours.&lt;br&gt;
If the speeds had been switched, he would have traveled at 80km/hr for 300 km (3.75 hours) and 100km at 100km/hr (1 hour); total time 4.75 hours.</PRE>