Two buses travel to a place at 45 km/hr and 60 km/hr respectively. If the second bus takes 1 5/2 hrs less

Question

Two buses travel to a place at 45 km/hr and 60 km/hr respectively. If the second bus takes \(5\frac12\) hrs less than the first for the journey, the length of the journey is 

(a) 900 km 

(b) 945 km 

(c) 990 km 

(d) 1350 km

Answer 1

(c) 990 km

Let the length of the journey be x km. Then,

\(\frac{x}{45}-\frac{x}{60}=\frac{11}{2}\) ⇒ \(\frac{4x-3x}{180}=\frac{11}{2}\) ⇒ \(\frac{x}{180}= \frac{11}{2}\)

⇒ x = \(\frac{11\times180}{2}\) = 990 km.