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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