Mary can clean the house in 6 hours. Her younger sister Ruth can do the same job in 9 hours. In how many hours can they do the job if they work together?
Use
time = 1/(1/M+1/R)
To find out how many hours it would take for Mary and Ruth to clean the house if they work together, we can use the concept of the work rate.
First, let's determine their individual work rates. Mary can clean the house in 6 hours, so her work rate is 1 house/6 hours. Ruth, on the other hand, can clean the house in 9 hours, so her work rate is 1 house/9 hours.
To combine their work rates, we add their individual rates. Mary's rate + Ruth's rate equals 1/6 + 1/9.
To simplify this expression, we need to find a common denominator. The least common multiple (LCM) of 6 and 9 is 18. We can convert the fractions to have a common denominator of 18.
1/6 = 3/18 (multiplying numerator and denominator by 3).
1/9 = 2/18 (multiplying numerator and denominator by 2).
Now we can add the fractions:
3/18 + 2/18 = 5/18.
Therefore, their combined work rate is 5/18 house per hour.
To determine the time it would take for them to clean the house together, we need to calculate the reciprocal of their combined work rate. The reciprocal of 5/18 is 18/5.
Hence, it would take Mary and Ruth approximately 18/5 hours, or 3 hours and 36 minutes, to clean the house if they work together.