How much time will it take these 5 people to build a house if they will work together from the start to the end?

Question

Anna can build a house in 1 year. Aly can build the same house in 2 years. Anton can build the same house in 3 years. Alexa can build the same house in 4 years. Alex can build the same house in 5 years. How much time will it take these 5 people to build a house if they will work together from the start to the end?

Answer 1

Individual build rates are:

George: 1    house per year

Greg:     1/2     "       "      "

Gabriel: 1/3     "       "      "

Glen:     1/4     "       "      "

Gordy:   1/5     "       "      "

If all 5 people work together, then you add together their individual build rates.

Group rate = 1 + 1/2 + 1/3 + 1/4 + 1/5 = 137/60  houses per year.

5 people build 137/60 houses per year,

Therefore, time to build one house is 60/137 years = 0.43796 yrs

Combined build time = 5 months, 7.7 days

Time required = 5mths, 8 days