Respuesta :
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 = [tex]\frac{\text{Distance traveled}}{\text{Speed}}[/tex]
= [tex]\frac{4x}{80}[/tex]
Similarly time taken to travel between station B and station C with speed 60 km per hour = [tex]\frac{x}{60}[/tex] km per hour
Now average speed between station A and station C = [tex]\frac{\text{Total distance between station A and station C}}{\text{time taken to travel}}[/tex]
= [tex]\frac{4x+x}{\frac{4x}{80}+\frac{x}{60}}[/tex]
= [tex]\frac{5x}{\frac{4x}{60} }[/tex]
= [tex]\frac{5\times 60}{4}[/tex]
= 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 = [tex]\frac{240t+60t}{(3t+t)}[/tex]
= [tex]\frac{300t}{4t}[/tex]
= 75 km per hour
