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.
Answers
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 taken
Let'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 km
Speed = 50 km/h
Time = Distance/Speed = 100/50 = 2 h
For the second part:
Let the speed of the train be 's' km/h
Distance = 100 km
Time = Distance/Speed = 100/s
Now, as we know that:
Average speed = Total distance traveled/ Total time taken
where, Average speed = 70 km/h
Total distance travelled = 200 km
Total time taken = 2 + 100/s
Substituting these values in the average speed equation, we get:
Average speed = Total distance traveled/ Total time taken
or, 70 = 200/ (2 + 100/s)
or, 70 × (2 + 100/s) = 200
or, 140 + 7000/s = 200
or, 7000/s = 60
or, s = 7000/60 = 116.67 km/h
Therefore, the speed of the train must be 116.67 km/h.