Question 1197471
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Edit: The distance doesn't need to be an integer, so the use of LCM is optional. The method I used works for any positive real number distance. I selected integers to make the numbers more digestible.


The use of the formulas mentioned by the other tutors is a great approach, if you understand what is going on, and understand how the formulas work.
I don't recommend blindly memorizing them unless you are under a time crunch (say for an upcoming exam).


I'll take a different approach.


The GCF of 24 and 16 is 8
The LCM of 24 and 16 is 24*16/GCF = 24*16/8 = 48


Let's say the distance from point A to B is 48 miles. 
There's nothing special about this value, so feel free to pick something else. 
I selected it so that the next two division operations result in whole numbers.


Going from A to B, the car travels 48 miles at a speed of 24 mph
distance = rate*time
time = distance/rate 
time = 48/24 
time = 2 hours.


Then when going from B to A, it travels a speed of 16 mph
time = distance/rate = 48/16 = 3 hours


The total distance is 48+48 = 96 miles for the entire round trip
The total time taken is 2+3 = 5 hours. We only account for traveling time and not moments when the car is stopped (eg: when the car is getting gas)


Then as the final step
distance = rate*time
rate = distance/time
rate = 96/5
rate = <font color=red>19.2 mph</font> as the final answer
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