Two buses start simultaneously from the same place towards a destination which is 180 km away. The first bus travels at a speed of 40 km/h and the second bus travels at a speed of 60 km/h. The second bus reaches the destination, waits for some time and returns back. If the buses cross each other 90 km away from the starting point, then for how long did the second bus wait at the destination?
- 20 minutes
- 36 minutes
- 45 minutes
- 1 hour
The Correct Option is B
Solution and Explanation
Distance covered by both buses together \(= \frac{180}{2} = 90 \text{ km}\)
Combined speed of both buses = 40 km/h + 60 km/h = 100 km/h
\(\text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{90 \text{ km}}{100 \text{ km/h}} = 0.9 \text{ hours} \text{ or } 54 \text{ minutes}\)
Time taken by bus B to reach the destination:
Distance = 180 km
Speed = 60 km/h
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{180 \text{ km}}{60 \text{ km/h}} = 3 \text{ hours}\)
Time taken by bus A to reach the destination:
Distance = 180 km
Speed = 40 km/h
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{180 \text{ km}}{40 \text{ km/h}} = 4.5 \text{ hours}\)
Time waited by bus B at the destination:
Total time taken by bus A = Time taken for both buses to meet + Time waited by bus B + Time taken by bus B to return to the meeting point.
4.5 hours = 0.9 hours + Time waited + 3 hours
Time waited = 4.5 hours - 0.9 hours - 3 hours
= 0.6 hours or 36 minutes.
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