Q.9 A bus moves from town A to town B with a uniform speed of 30Km/h. Find the speed which the bus should acquire while moving from town B to town A so that the average speed of the whole journey of bus is 40Km/h. Also find the average velocity of the whole journey.

Q.9 A bus moves from town A to town B with a uniform speed of 30Km/h.

1.	Q.9 A bus moves from town A to town B with a uniform speed of 30Km/h. Find the speed which the bus should acquire while moving from town B to town A so that the average speed of the whole journey of bus is 40Km/h. Also find the average velocity of the whole journey.
Answer» Answer: For a distance of 200km between Delhi and Agra, a train travelling at a speed of 50km/h for the first 100KM, the train must travel at 116.67 km/h for the next 100km so that the average speed for the whole journey is 70km/h.To find the average speed we need to use the relation:Average speed = Total distance TRAVELED/ Total time takenLet's now consider the conditions given in the question to find the required value.Explanation:Let's find the time taken by train to travel each part of the distance.For the first part:Distance = 100 kmSpeed = 50 km/hTime = Distance/Speed = 100/50 = 2 hFor the second part:Let the speed of the train be 's' km/hDistance = 100 kmTime = Distance/Speed = 100/sNow, as we KNOW that:Average speed = Total distance traveled/ Total time takenwhere, Average speed = 70 km/hTotal distance travelled = 200 kmTotal time taken = 2 + 100/sSubstituting these VALUES in the average speed equation, we get:Average speed = Total distance traveled/ Total time takenor, 70 = 200/ (2 + 100/s)or, 70 × (2 + 100/s) = 200or, 140 + 7000/s = 200or, 7000/s = 60or, s = 7000/60 = 116.67 km/hTherefore, the speed of the train must be 116.67 km/h.