A bus takes two hours less for a journey of 300 km, if its speed is increased by 5 km/hr from its normal speed. The normal speed is.
25 km/hr
Let the normal speed of the bus be v km/hr.
Time taken at normal speed for the 300 km journey = 300/v hours.
Time taken at the increased speed (v + 5) km/hr = 300/(v + 5) hours.
Since the increased speed saves 2 hours, we can write the equation: 300/v − 300/(v + 5) = 2.
Taking a common denominator: 300(v + 5) − 300v = 2v(v + 5), which simplifies to 300 × 5 = 2v(v + 5), i.e., 1500 = 2v² + 10v.
Dividing both sides by 2: v² + 5v − 750 = 0.
Using the quadratic formula, v = [−5 ± √(25 + 3000)]/2 = [−5 ± √3025]/2 = [−5 ± 55]/2.
Taking the positive root: v = 50/2 = 25.
Therefore, the normal speed of the bus is 25 km/hr.
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