Question

AQ1- On a 100km track a train travels the first 30km at a uniform speed of 30 km/h. How fast must the train travel the next 70 km so as to average 40 km/h for the entire trip?

Answer 1

Given 
d1 = 30 km
s1 = 30km/h
⇒t1 = d1/s1 = 30km/30km/h = 1h
d2 = 70 km
Avg Speed = 40 km/h

Avg Speed = d1 + d2/t1 + t2
⇒ 40 km/h = 100km/1h + t2
⇒40 km/h(1h + t2) = 100 km/h 
⇒1h + t2 = 100 km/h / 40 km/h
= 2.5h
⇒t2 = 1.5h
s2 = d2/t2 = 70km/1.5h = 46.67 km/h

Answer 2

ᴀɴsᴡᴇʀ                                                            

                            ɪɴ ᴛʜᴇ ғɪʀsᴛ ᴋᴍ sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ᴛʀᴀɪɴ, ᴠ1 = 30 ᴋᴍ/ʜ                            

                            sᴘᴇᴇᴅ ᴏғ ᴛʜᴇ ᴛʀᴀɪɴ ɪɴ ᴛʜᴇ ɴᴇxᴛ 90 ᴋᴍ, ᴠ2                            

                           ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ = ᴋᴍ/ʜ = (ᴠ + ᴠ)/2                                                                              

→ ᴠ2 = 90 ᴋᴍ/ʜ