Question : A man travels for 5 hours and 15 minutes. If he covers the first half of the journey at 60 km/h and rest at 45 km/h. Find the total distance travelled by him.
Option 1: $1028\frac{6}{7}$ km
Option 2: $189$ km
Option 3: $378$ km
Option 4: $270$ km
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Correct Answer: $270$ km
Solution : Let the total distance be $2d$ km. The man travels at 60 km/h for the first half. So time to travel first half = $\frac{d}{60}$ The man travels at 45 km/h for the second half. So time to travel second half = $\frac{d}{45}$ The total time taken to complete the journey is 5 hours 15 minutes or, $5\frac{1}{4}$ hours or $\frac{21}{4}$ hours. According to the question, $\frac{d}{60}+\frac{d}{45}=\frac{21}{4}$ ⇒ $\frac{7d}{180}=\frac{21}{4}$ So, $d$ =135 km. Therefore, total distance = $2d$ = 2 × 135 = 270 km. Hence, the correct answer is $270$ km.
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