### Brain Teasers

# Building a house

Joe and Bob can build a house together in 45 days. Bob works exactly half the speed that Joe does. How many days can Joe and Bob each build a house on their own?

### Answer

Since it takes them 45 days together to build one house, they can build 1/45 of a house in one day. Therefore you can set up an equation to add up each person's contribution to this 1/45 of a house:1/x + 1/2x = 1/45

Since the fractions on the left side of the equation represent each person's contribution, solving for x and then inverting each fraction will give their output in days/house:

Joe takes 67.5 days and Bob takes 135 days.

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