Answer:
(i). Average speed = 75 km per hour
(ii). Average speed = 75 km per hour
Step-by-step explanation:
This question is incomplete; here is the complete question.
A train traveled from station A to station B at an average speed of 80 kilometers per hour and then from station B to station C at an average of 60 kilometers per hour. If the train did not stop at station b, what was the average speed at which the train traveled from station A to C?
(i). The distance that the train traveled from station A to station B was 4 times the distance that train traveled from station B to station C.
(ii). The amount of time it took to the train to travel from station A to station B is 3 times the amount of time that it took the train to travel from station B to station C.
(i) Let the distance between station B and station C = x km
So the distance between Station A and station B = 4x km
Therefore, time to travel the distance x km with 80 km per hour = ![\frac{\text{Distance traveled}}{\text{Speed}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BDistance%20traveled%7D%7D%7B%5Ctext%7BSpeed%7D%7D)
= ![\frac{4x}{80}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%7D%7B80%7D)
Similarly time taken to travel between station B and station C with speed 60 km per hour =
km per hour
Now average speed between station A and station C = ![\frac{\text{Total distance between station A and station C}}{\text{time taken to travel}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BTotal%20distance%20between%20station%20A%20and%20station%20C%7D%7D%7B%5Ctext%7Btime%20taken%20to%20travel%7D%7D)
= ![\frac{4x+x}{\frac{4x}{80}+\frac{x}{60}}](https://tex.z-dn.net/?f=%5Cfrac%7B4x%2Bx%7D%7B%5Cfrac%7B4x%7D%7B80%7D%2B%5Cfrac%7Bx%7D%7B60%7D%7D)
= ![\frac{5x}{\frac{4x}{60} }](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B%5Cfrac%7B4x%7D%7B60%7D%20%7D)
= ![\frac{5\times 60}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Ctimes%2060%7D%7B4%7D)
= 75 km per hour
(ii). Let the train took the time to cover the distance between station B and station C = t hours
Therefore, time taken by the train between station A and B = 3t
Distance between Station A and station B = Speed × time
= 80 × 3t
= 240t km
Similarly distance between station B and station C = 60 × t
= 60t
Now average speed between station A and station C = ![\frac{240t+60t}{(3t+t)}](https://tex.z-dn.net/?f=%5Cfrac%7B240t%2B60t%7D%7B%283t%2Bt%29%7D)
= ![\frac{300t}{4t}](https://tex.z-dn.net/?f=%5Cfrac%7B300t%7D%7B4t%7D)
= 75 km per hour