During a drought, 50 people have only $1000 \mathrm{~L}$ of water left. If every person consumes an identical amount of water, the 1000-liter supply would be exhausted in one day. If 40 people were to leave, how much longer (in days) would the water supply last?
I noticed people*days=constant. Why is that true in these more people is worse problems?
For example, 1 person can last on 1000L on fifty days, but 40 people can last on 1000L for 5/4 days.
Clearly you only gain 1/4 of a day.
This doesn't make sense because the answer key says 40 people can last 4 more days than 50 people on 1000L.
You have calculated the extra days with respect to $40$ people left, but the question asks you to consider $10$ remaining, which is why you got that incorrect figure. If $50$ people get through $1000$ litres of water a day then that means each person consumes $20$ litres of water a day. If $40$ people leave then that means there are $10$ people left, and since their rate of consumption doesn't change, it means they get through $200$ litres of water a day. With a supply of $1000$ litres, $10$ people will take $\frac{1000}{200}= 5$ days to drink it all. This is an increase of $4$ days.