Let's solve this problem step by step. We are given that a car travels from Calabar to Enugu, a distance of \(P\) km with an average speed of \(U\) km per hour and continues to Benin, a distance of \(Q\) km, with an average speed of \(W\) km per hour. We are asked to find its average speed from Calabar to Benin.

The average speed is defined as the total distance traveled divided by the time taken to travel that distance. The total distance traveled from Calabar to Benin is \(P + Q\) km. The time taken to travel from Calabar to Enugu is \(\frac{P}{U}\) hours, and the time taken to travel from Enugu to Benin is \(\frac{Q}{W}\) hours. So, the total time taken to travel from Calabar to Benin is \(\left(\frac{P}{U}\right) + \left(\frac{Q}{W}\right)\) hours.

Therefore, the average speed from Calabar to Benin is:

Average speed = Total distance / Total time

= \(\frac{(P + Q)}{\left(\frac{P}{U}\right) + \left(\frac{Q}{W}\right)}\)

= \(\frac{(P + Q)}{\left(\frac{PW + QU}{UW}\right)}\)

= \(\frac{UW(P + Q)}{(PW + QU)}\)

So, the average speed from Calabar to Benin is \(\frac{UW(P + Q)}{(PW + QU)}\).