A car travels from A to B First half of the distance it move

A car travels from A to B. First half of the distance it moves with a speed 60 mph, and the second half - with a speed 40 mph. Find the average speed of a car for the whole trip.

Solution

Let x = total distance from A to B
then
\"time traveled 1st half\" = (x/2)/60 = x/120
\"time traveled 2nd half\" = (x/2)/40 = x/80
.
Total time: x/120 + x/80
.
Average speed is
\"total distance\"/\"total time\"
= x/(x/120 + x/80)
Dividing numerator and denominator by \'x\':
= 1/(1/120 + 1/80)
= 10/(1/12 + 1/8)
= 10/(2/24 + 3/24)
= 10/(5/24)
= 240/5
= 48 mph