What is the correct way to estimate the work done by a climber?

My teacher gave us a worksheet with word problems and their solutions. It is in German, so I have tried my best to translate it to English:

A 26 year old man climbs Mount Everest (8848 m) in only 8 hours 10 mins from the base camp at 5300 m. Estimate the "lifting work" (Hubarbeit) that the man exerted in the climb.

I thought to use the formula: $W = F \cdot \Delta S$, but I don't know what $F$ would be. I think the $\Delta S$ is $8848 - 5300 = 3548$. But then I looked at the solutions and my teacher used this formula: $W = m g h$. He guessed the man's weight and also used $g = 10\ \mathrm{N}/\mathrm{kg}$. I don't understand this.

Could someone maybe help me? Anyone have an idea?

"Estimate the 'lifting work'" is the key part. Well, what is the lifting work? What are you lifting against? Gravity. What's the force gravity exerts? $F_{gravity} = mg$ (neglecting variations in $g$ as you go up the mountain). Therefore, the force in your formula $W=F\cdot \Delta S$ is the force of gravity.
$W=mgh$ is the potential energy the climber (of mass $m$) gains by changing his altitude by $h=8848~\textrm{m} - 5300~\textrm{m} = 3548~\textrm{m}$.
He's asking for "lifting work", work in the vertical direction. If we assume he's not accelerating up Everest, his vertical work will be opposing gravity, so $$F_{Lifting} = mg$$ and $$W_{Lifting} = F_{Lifting} \Delta h = (mg)\Delta h$$