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Two bullets are fired at an interval of 15 minutes but a  bus approaching the place of firing hears the second bullet after 14.5 minutes. If the speed of sound is 330 meters per second, what is the speed of the Bus?

Two bullets are fired at an interval of 15 minutes but a  bus approaching the place of firing hears the second bullet after 14.5 minutes. If the speed of sound is 330 meters per second, what is the speed of the Bus? Correct Answer 41 km/hr

Two bullets are fired at an interval of 15 minutes.

Speed of sound = 330 m/s

Formula

Speed of bus × Time after which bullet sound heard = Speed of sound × Difference in time of bullet fired and the sound heard

Calculation

14.5 min = 870 sec

Speed of bus × 870 = 330 × 30

⇒ Speed of bus = (330 × 30)/870 m/s

⇒ Speed of bus = (330 × 30)/870 × (18/5) ≈ 41 km/hr

Detailed Method

15 min = 15 × 60 = 900

14.5 min = 870 sec

Total distance covered by the sound of 1st bullet - Total distance covered by the sound of 2nd bullet = Total distance covered by bus

⇒ (330 × 900) - (330 - 870) = Speed of bus × 870

⇒ 330 × (900 - 870) = Speed of bus × 870

⇒ 330 × 30 = Speed of bus × 870

⇒ Speed of bus = (330 × 30)/870 m/s

⇒ Speed of bus = (330 × 30)/870 × (18/5) = 40.96 ≈ 41 km/hr

Important Points

The distance covered by bus in 14.5 minutes is same as the  distance covered by the bullet in (15 - 14.5) minutes i.e. 30 seconds 

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