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.
Important Questions from Speed Time and Distance
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
