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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Comments
Good question. A nice twist from the usual opposite problem of how long do they take together.
Imagine the frame is prebuilt and only has to be nailed together. Bob puts in 1 nail per day while Joe puts in 2 nails per day = 3 nails per day = 135 nails to make a house.
Bob on his own then puts in 1 per day = 135 days. Joe puts in 2 per day = 135/2=67.5 days (no algebra!)
Imagine the frame is prebuilt and only has to be nailed together. Bob puts in 1 nail per day while Joe puts in 2 nails per day = 3 nails per day = 135 nails to make a house.
Bob on his own then puts in 1 per day = 135 days. Joe puts in 2 per day = 135/2=67.5 days (no algebra!)
I think it should be 22.5 for Joe and 45 for Bob. Because no matter how fast the fastest person goes it will stil take Bob 45 days to finish his part of the house.
Not easy but i got it . And the answer is right because Bob builds 1/3 of the house in 45 days so takes 3 times as long to build a full house and Joe builds 2/3 of the house working twice as fast as Bob in the same time and so takes 1.5 times longer to build a house on his own.
sorry if that confused anyone
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