If Tim can paint a house in 6 hours, and Tom can paint the same house in 4 hours, how long will it take if they paint together?
2.5 hours
3 hours
2.4 hours
3.6 hours
To solve this problem, we can use the formula:
(1/Tim's rate) + (1/Tom's rate) = (1/combined rate)
Tim's rate is 1 house/6 hours, so his rate is 1/6 houses per hour.
Tom's rate is 1 house/4 hours, so his rate is 1/4 houses per hour.
Substituting the rates into the formula:
(1/6) + (1/4) = (1/combined rate)
Multiplying through by 12 to remove the denominators:
2 + 3 = (12/combined rate)
5 = (12/combined rate)
12/5 = combined rate
Therefore, the combined rate is 12/5 houses per hour.
To find out how long it will take to paint the house together, we need to find the reciprocal of the combined rate:
(combined rate) = 5/12 houses per hour.
Therefore, it will take (12/5) hours to paint the house together.
Converting this to a decimal:
12 ÷ 5 = 2.4 hours.
Answer: It will take 2.4 hours for Tim and Tom to paint the house together.