Question : During a journey, a person travels half of the distance at a speed of 18 km/h and the remaining half of the journey at a speed of 22 km/h. What is his average speed for the entire journey?
Option 1: 21.4 km/h
Option 2: 20.2 km/h
Option 3: 19.2 km/h
Option 4: 19.8 km/h
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Correct Answer: 19.8 km/h
Solution : Let $d$ be the total distance of the journey. Half of the distance at 18 km/h and the remaining half at 22 km/h ⇒ Total Time for the journey = $\frac{d}{2×18}$ +$\frac{d}{2×22}$ ⇒ average Speed = $\frac{\text{d}}{\text{$\frac{d}{2×18}$ +$\frac{d}{2×22}$ }}$ = $\frac{\text{d}}{\text{$\frac{22d}{2×18×22}$ +$\frac{18d}{2×18×22}$ }}$ = $\frac{d}{\frac{40d}{2×18×22}}$ = $\frac{18×22}{20}$ = 19.8 Hence, the correct answer is 19.8 km/h.
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