Tuesday Tangle – Time to hire a Maid

Gentle Reader,

I was once again thwarted by this week’s Tangle. This is one of those puzzles where it just doesn’t seem as if the solution should work – but it does, and it’s incredibly simple...

Time to hire a Maid

Two flatmates, Andrina and Luke, hate housework. One Saturday morning, when their flat is in a terrible state, they finally decide to tackle the mess head on.

They have three tasks:

Wash the dishes.

Mow the lawn.

Vacuum the carpets.

They have only one vacuum cleaner, one lawn mower and one sink with room for one person. Each task, when done by one person, takes one hour. What is the shortest amount of time Andrina and Luke will need to complete the tasks?

(Solution below)

Solution (hold down mouse button and scroll over to reveal): Andrina and Luke can complete all the chores in 90 minutes. Each should complete half of a task at the same time and then alternate the tasks. So:

Luke washes the dishes and Andrina mows the lawn for 30 minutes – dishes half washed; lawn half mowed.

Then Luke mows the lawn and Andrina vacuums the carpet for 30 minutes – dishes half washed; lawn fully mowed; carpets half vacuumed.

Luke vacuums the carpet and Andrina washes the dishes for 30 minutes – dishes completely washed; lawn fully mowed; carpets fully vacuumed.