A cyclist rides 24 km at 16 kmph and further 36 km at 15 kmph. Find his average speed for the journey. (R.R.B., 2008)

### Concept & Average Speed Average speed is calculated by dividing the total distance traveled by the total time elapsed. $$Average\ Speed = \frac{Total\ Distance}{Total\ Time}$$ ### Step-by-Step Solution * **Step 1: Calculate Total Distance.** * Total Distance $= 24$ km $+ 36$ km $= 60$ km. * **Step 2: Calculate the time taken for each segment.** * Time 1 $= \frac{Distance_1}{Speed_1} = \frac{24}{16} = 1.5$ hours. * Time 2 $= \frac{Distance_2}{Speed_2} = \frac{36}{15} = \frac{12}{5} = 2.4$ hours. * **Step 3: Calculate Total Time.** * Total Time $= 1.5 + 2.4 = 3.9$ hours. * **Step 4: Calculate Average Speed.** * Average Speed $= \frac{60}{3.9} = \frac{600}{39}$ * Simplify the fraction by dividing numerator and denominator by 3: $\frac{200}{13}$ * Calculate the decimal: $200 \div 13 \approx 15.3846...$ kmph. ### Exam Strategy & Shortcut Recognize that $\frac{24}{16}$ and $\frac{36}{15}$ yield simple decimals ($1.5$ and $2.4$). Adding these directly to get $3.9$ hours is much faster than cross-multiplying fractions to find a common denominator. ### Common Pitfall Choosing "None of these" because $15.3846...$ does not terminate perfectly, failing to recognize that $15.38$ is standard two-decimal place rounding for this exact value. ### Final Answer Therefore, the correct answer is **15.38 kmph**.