If a man travels p hours at an average rate of q miles per hour, and then r hours at an average rate of s miles per hour, what is his overall average rate of speed?

Total miles traveled in p hours = p*q miles and

Total miles traveled in r hours = r*s miles

so, average rate of speed = total miles traveled / number of hours

=[{ (p*q) + (r*s) } / (p+r) ] miles per hour