Amy paints a house in 4 hours and Thomas paints the same house in 6 hours. How long will it take to paint the house together?
Here's one of Bobpursley's answers to this question.
http://www.jiskha.com/display.cgi?id=1243466404
Amy's rate is 1/4 house per hour.
Thomas' rate is 1/6 house per hour.
The RATES are what get added when you want to know how fast they can do a job together. The combined rate is 1/4 + 1/6 = 5/12 houses per hour.
The time to do one house is 1 house divided by the rate (5/12 houses/hr), or 12/5 hours. That's 2 hours and 24 minutes.
To find out how long it will take to paint the house together, we can use the formula:
1 / (1/A + 1/B) = Time
where A is the amount of time it takes Amy to paint the house (4 hours) and B is the amount of time it takes Thomas to paint the house (6 hours).
1 / (1/4 + 1/6) = Time
First, we need to find the common denominator of the fractions (4 and 6). The common denominator is 12.
1 / (3/12 + 2/12) = Time
Now, let's add the fractions:
1 / (5/12) = Time
To divide a number by a fraction, we can multiply it by the reciprocal of the fraction:
1 * (12/5) = Time
Now, let's simplify the multiplication:
12/5 = Time
So, it will take 12/5 or 2.4 hours to paint the house together.