Washing elephants
Problem
Mary and Nigel look after elephants in a zoo.
Mary takes 50 minutes to wash an elephant and Nigel takes 40 minutes to wash an elephant.
If they wash an elephant together, how long will it take them?
This problem is taken from the World Mathematics Championships
Student Solutions
Answer: 22$\frac29$ minutes
Scaling up to more elephants
Mary: 50 minutes 1 elephant 200 minutes 4 elephants
Nigel: 40 minutes 1 elephant 200 minutes 5 elephants
Together: 200 minutes 9 elephants
200$\div$9 minutes 1 elephant
200$\div$9 = 22$\frac29$
Seeing how much of the elephant is clean after 10 minutes (or 5, or 20, etc)
Mary: 50 minutes 1 elephant 10 minutes $\frac15$ elephant
Nigel: 40 minutes 1 elephant 10 minutes $\frac14$ elephant
Together: 10 minutes $\frac15+\frac14=\frac9{20}$ elephant
10$\div$9 minutes $\frac1{20}$ elephant
200$\div$9 minutes 1 elephant
200$\div$9 = 22$\frac29$