to a painter can finish painting a house in 8 hours. Her assistant takes 10 hours to finish the same job. How long would it take for them to complete the job if they were working together? a. 9/40 hours b. 7 hours c. 9 hours d. 4 4/9 hours

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to a painter can finish painting a house in 8 hours. Her assistant takes 10 hours to finish the same job. How long would it take for them to complete the job if they were working together? a. 9/40 hours b. 7 hours c. 9 hours d. 4 4/9 hours

Mathematics
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the painter paints at the rate 1 house per 8 hours; the assistant paints at the rate 1 house per 10 hours. The combined rate is 1/8+1/10 = 10/80+8/80 = 18/80 = 9/40 houses per hour.
9/40 of the house is done in one hour; how many hours to finish the house?
4 hours is 36/40; just got 4/40 left = 1/10 of an hour

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\[rate={amount \over time} '\rightarrow' 'time={amount \over rate} = {{1'house}\over \left(9'houses \over 40'hours \right)} = {40 \over 9} hours\] \[{40 \over 9} = {9 \cdot 4 + 4 \over 9} = 4{4 \over 9}\] You can find bounds easily - it's less than half the time of the slower one, and more than half the time of the faster one, so between 4 and 5 hours.
thanks a bunch :D

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