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?

A (pq+rs)/(p+r)

B (q+s)/2

C (q+s)/(p+r)

D (p/q)+(r/s)

Correct Answer: Option A

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

Total miles traveled in r hours = r x s miles

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

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