JAMB Mathematics 2021 Paper

Concept:Average speed is the total distance travelled divided by the total time taken for the whole journey.Explanation:From Calabar to Enugu, the distance is $P$ km and the speed is $U$ km/h.So the time for this part is $t_1 = \frac{P}{U}$ hours.From Enugu to Benin, the distance is $Q$ km and the speed is $W$ km/h.So the time for this part is $t_2 = \frac{Q}{W}$ hours.The total distance from Calabar to Benin is $P + Q$ km.The total time for the whole journey is:$$t_1 + t_2 = \frac{P}{U} + \frac{Q}{W}$$Hence the average speed is:$$\text{Average speed} = \frac{P+Q}{\frac{P}{U} + \frac{Q}{W}}$$Simplify the denominator using the common denominator $UW$:$$\frac{P}{U} + \frac{Q}{W} = \frac{PW + QU}{UW}$$Therefore:$$\text{Average speed} = \frac{P+Q}{\frac{PW+QU}{UW}} = \frac{UW(P+Q)}{PW+QU}$$This matches the form given in option B.Answer:$$\frac{UW(P+Q)}{PW+QU}$$Option B.