Question

a train travels the first 30 km of 120 km track with a uniform speed of 30km/h.what should be the speed of train to cover the remaining distance of the track so that its average speed is 60 km/h for the entire trip.

Answer 1

To travel 120km at a speed of 60km/hr the train will take 2hrs to reach destination
Now train spent 1hr to travel 30km
Distance left to travel= 120-30 = 90km
Time left 1hr therefore train needs to travel at 90km/hr to have avg speed of 60km/hr

Answer 2

ᴀɴsᴡᴇʀ                                                            

                            ɪɴ ᴛʜᴇ ғɪʀsᴛ ᴋᴍ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ᴛʀᴀɪɴ, ᴠ = ᴋᴍ/ʜ                            

                            sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ᴛʀᴀɪɴ ɪɴ ᴛʜᴇ ɴᴇxᴛ ᴋᴍ, ᴠ (ᴛᴏ ʙᴇ ᴅᴇᴛᴇʀᴍɪɴᴇᴅ)                            

                           ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ = ᴋᴍ/ʜ = (ᴠ + ᴠ)/                                            

                                                       = ( ᴋᴍ/ʜ + ᴠ)/                                  

→ ᴠ = ᴋᴍ/ʜ