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 speed 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 Station C?

Answer 1

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 = $\frac{\text{Distance traveled}}{\text{Speed}}$

= $\frac{4x}{80}$

Similarly time taken to travel between station B and station C with speed 60 km per hour = $\frac{x}{60}$ km per hour

Now average speed between station A and station C = $\frac{\text{Total distance between station A and station C}}{\text{time taken to travel}}$

= $\frac{4x+x}{\frac{4x}{80}+\frac{x}{60}}$

= $\frac{5x}{\frac{4x}{60} }$

= $\frac{5\times 60}{4}$

= 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 = $\frac{240t+60t}{(3t+t)}$

= $\frac{300t}{4t}$

= 75 km per hour