Recipe for a hill climb

Ingredients: one hill six hundred metres high, one pair of good legs that climb three hundred metres every hour, and one sunset at seven in the evening. The climb takes six hundred divided by three hundred, which is two hours.

Ingredients: a hill $h=600$ m high, legs that climb $v=300$ m/h, a sunset at $19:00$. The climb: $t=\frac{h}{v}=600÷300=2$ h.

$h=600\mathrm{m}$, $v=300m/h$: $t=\frac{h}{v}=2\mathrm{h}$.

Going down is twice as fast, so one hour. Add half an hour of rest at the top. The whole trip is two plus one plus a half, which is three and a half hours.

Down is twice as fast: $2÷2=1$ h. Rest at the top: $0.5$ h. The whole trip: $2+1+0.5=3.5$ h.

$2÷2=1$ and $2+1+0.5=3.5\mathrm{h}$.

Add one hour for safety, which makes four and a half hours. Count back from the sunset: seven o'clock minus four and a half hours is half past two. Do not start later than that.

One safety hour: $3.5+1=4.5$ h, that is $4:30$. Count back from the sunset: $19:00-4:30=14:30$. Do not start later than that.

$3.5+1=4.5\mathrm{h}$; $19:00-4:30=14:30$.

The secret ingredient is a turn-back time. You start at half past two and the climb takes two hours, so you must be at the top by half past four. If you are not, turn round: the hill will be there tomorrow too.

The secret ingredient is a turn-back time. Start $14:30$, climb $2$ h: $14:30+2:00=16:30$. If your time at the top is not $T\le 16:30$, turn round: the hill will be there tomorrow too.

$14:30+2:00=16:30$; turn round $R$: $T>16:30\Rightarrow R$.