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Mowing The Lawn

Problem

Matilda's father takes 20 minutes to mow the back garden lawn, but Matilda takes 30 minutes to do the same job. If they worked together, how long would it take to cut the lawn?


Solution

If Matilda takes 30 minutes to mow 1 lawn, she could mow 2 lawns in 60 minutes. Her father, who takes 20 minutes to mow 1 lawn, could mow 3 lawns in 60 minutes. So both of them could mow 5 lawns in 60 minutes.

Hence they would take 12 minutes to mow the lawn between them.

If Matilda took 25 minutes by herself and her father took 15 minutes, how long would it take them if they worked together?
Can you generalise?

Problem ID: 64 (Feb 2002)     Difficulty: 1 Star

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