On a drive from your home to town, you

Question

wish to average 52 mph. The distance from
your home to town is 106 miles. However,
at 53 miles (half way), you find you have
averaged only 39 mph.
What average speed must you maintain in
the remaining distance in order to have an
overall average speed of 52 mph?
Answer in units of mph

Answer 1

To drive 106 miles at an average speed of 52 mph requires a total driving time of
106/52 = 2.03846 hours.

If you drive the first 53 miles at an average speed of 39 mph, you have used up 53/39 = 1.35897 hours

You still need to cover 53 miles in the remaining time available, 0.67949 hrs.
That means that you have to average
53/0.67949 = 80.000 mph during the last half.