Question : Two buses travel to a place at 45 km/hr and 60 km/hr, respectively. If the second bus takes $5\frac{1}{2}$ hours less than the first for the journey, then the length of the journey is:
Option 1: 900 km
Option 2: 945 km
Option 3: 990 km
Option 4: 1350 km
Correct Answer: 990 km
Solution :
Given: The speeds of the two buses are 45 km/hr and 60 km/hr, respectively.
The second bus takes $5\frac{1}{2}$ hours less than the first bus.
Let the length of the journey be $x$ km.
According to the given condition,
$⇒ \frac{x}{45}-\frac{x}{60}=\frac{11}{2}$
$⇒ \frac{4x-3x}{180}=\frac{11}{2}$
$⇒ \frac{x}{180}=\frac{11}{2}$
$\therefore x= 90 × 11 = 990$ km
Hence, the correct answer is 990 km.
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