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

(i). Average speed = 75 km per hour

(ii). Average speed = 75 km per hour

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}}`

=
`(4x)/(80)`

Similarly time taken to travel between station B and station C with speed 60 km per hour =
`(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}}`

=
`(4x+x)/((4x)/(80)+(x)/(60))`

=
`(5x)/((4x)/(60) )`

=
`(5* 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 =
`(240t+60t)/((3t+t))`

=
`(300t)/(4t)`

= 75 km per hour