Question 1014794
Let x = constant original speed, in miles per hour.

Then for first 105 miles, with a rate of x mph, the time traveled was 105/x hours.  (From the formula t = distance/speed.)

The last 42 miles was traveled at a rate of x/2 mph as given, so the time traveled is {{{42/(x/2)}}}, or 84/x hours.

Hence, as mentioned in the problem, {{{105/x+ 84/x = 2.7}}}

{{{189/x = 2.7}}}
{{{x/189 = 1/2.7}}}
{{{x = 189/2.7}}}, after cross-multiplication.

Thus, x = 70 mph, the original speed.