The night bus

The night bus leaves at half past ten in the evening and arrives at a quarter past six in the morning. That is seven hours and forty-five minutes, and the driver stops three times for fifteen minutes each.

Leaves at $22:30$, arrives at $6:15$: $90+375=465$ min, that is $7$ h $45$ min. Three stops: $3\times 15=45$ min.

$22:30\to 6:15$ is $90+375=465^{\prime }$. Stops: $3\times 15=45^{\prime }$.

So the bus is really moving for seven hours. At sixty kilometres an hour that makes four hundred and twenty kilometres, and half of the way is two hundred and ten.

Moving time: $465-45=420$ min, that is $7$ h. At $v=60$ km/h the distance is $d=vt=60\times 7=420$ km. Half of the way: $420÷2=210$ km.

$465-45=420^{\prime }$, that is $7$ h. $v=60$: $d=vt=60\times 7=420\mathrm{km}$, half: $420÷2=210$.

I woke at two in the morning, sure we were nearly there. One stop was behind us, so we had been moving for three hours and a quarter, which is one hundred and ninety-five kilometres. We had not even reached the middle.

I woke at $2:00$, $210$ min after the start. One stop was done, so we had moved $210-15=195$ min, that is $3.25$ h. Distance: $60\times 3.25=195$ km, and $195<210$. Not even half way.

At $2:00$ we had moved $210-15=195^{\prime }$. $d=60\times 3.25=195<210$.

Two hundred and twenty-five kilometres were left: three and three quarter hours of driving, plus two stops, so four hours and a quarter. Two o'clock plus that is a quarter past six. I went back to sleep.

Left: $420-195=225$ km, so $225÷60=3.75$ h of driving. With $2$ stops: $225+30=255$ min, that is $4$ h $15$ min. And $2:00+4:15=6:15$. Back to sleep.

$420-195=225$, $225÷60=3.75$ h; $225^{\prime }+2\times 15^{\prime }=255^{\prime }$, and $2:00+4:15=6:15$.