Detailed explanation would be appreciated

So the bus is initially going at 39km/hr but we want it in minutes, so divide by 60 to get that the bus goes .65 km/min. It does this for 20 minutes so multiply .65 by 20 and it has gone 13km in the first 20 minutes. It then goes 12km/hr, again divide by 60 to get .2km/min, it goes this fast for 10 minutes so it goes 2km in 10 minutes. At this point the bus has gone 15km, we know that his house is 30km away from the school so this tells us the bus will go 30km/hr (.5km/min) for 15km, taking it 30 minutes. It takes the bus one hour to get home.
His mom travels at a constant speed of 45km/hr (0.75km/min) the whole 30km to her home. Take the 30km and divide it by 0.75 to find that it took her 40 minutes to drive home BUT she didn't leave the school until 30min after the bus left, so her total time is 1hr10min.
She will not get home in time, she will be 10min late