Question

On a 120 km track a train travelsthe first 30 km at uniform speed 30 km/h how fast must the train travel in next 90 km so at the average speed of 60 km/h for the entire trip

Answer 1

Hey friend
here is your answer

total distance = 120 km
average speed = 60 km/hr

I case

distance = 30 km
speed = 30 km/ hr
so,
time = 30 / 30 = 1 hr

II case

distance = 90 km
speed = x ( let )
so,
time = (90 / x ) hr


$average \: speed = \frac{total \: distance}{ \: total \: time} \\ so \\ 60 = \frac{120}{1 + \frac{90}{x} } \\ 1 + \frac{90}{x} = \frac{120}{60} \\ 1 + \frac{90}{x} = 2 \\ \frac{90}{x} = 2 - 1 \\ x = 90km {hr}^{ - 1}$
speed at II case = 90 km/hr

glad to help you
hope it helps
thank you.

Answer 2

                           ANSWER                            

                          In the first 30 km speed of the train, v1 = 30 km/h

                          Speed of the train in the next 90 km, v2 (to be determined)

                         Average speed = 60 km/h = (v1 + v2)/2  

                                         = (30 km/h + v2)/2  

                              → v2 = 90 km/h