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Packing Boxes

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

In one hour, Harry and Christine together pack $18$ boxes. Harry and Betty together pack $12$ boxes. Christine and Betty together pack $9$ boxes.

Therefore Harry packs $3$ more boxes than Christine, looking at the rates when they're each with Betty.

In one hour Christine would therefore pack $7\frac{1}{2}$ boxes.

This problem is taken from the UKMT Mathematical Challenges.