Working alone it takes Jerry 9 hrs to mop a warehouse. Ruth can mop the same warehouse in 10 hrs. If they worked together how long would it take them?
Jerry does 1/9 of the work in one hour.
Ruth does 1/10 of the work in one hour.
Together they do 1/9+1/10 = 19/90 of the work in one hour.
How long would it take them together to finish the work ?
To solve this problem, we can use the concept of work rates.
First, let's find Jerry's work rate. Since it takes him 9 hours to mop the warehouse alone, his work rate is 1/9 of the warehouse per hour. This means that Jerry can mop 1/9 of the warehouse in 1 hour.
Similarly, Ruth's work rate is 1/10 of the warehouse per hour. Meaning, she can mop 1/10 of the warehouse in 1 hour.
To find out how long it would take them to mop the warehouse together, we need to add up their work rates.
Jerry's work rate + Ruth's work rate = (1/9 + 1/10) of the warehouse per hour.
To add the fractions, we need a common denominator, which in this case is 90. So,
(1/9 + 1/10) = (10/90 + 9/90) = 19/90 of the warehouse per hour.
Now, since we want to know how long it would take them to mop the entire warehouse, we can divide the total work of the warehouse (1 whole unit) by their combined work rate.
1 (whole unit) / (19/90) of the warehouse per hour
To divide by a fraction, we multiply by its reciprocal:
1 x (90/19) = 90/19 hours.
Therefore, it would take Jerry and Ruth approximately 90/19 hours, or approximately 4.74 hours, to mop the warehouse if they worked together.