it takes janet 9 hours to do a task and it take jancie 10 hours to do the same task how long will it take both of them to do the task together
janet rate: 1task/9hrs
jancie rate: 1task/10hrs
combinded rate=1task/hr (1/9+1/10)
timecombined=1task/combinded rate
careful with the fractions.
5 hrs
To find out how long it will take both Janet and Jancie to do the task together, we can use the concept of rates.
First, let's find their individual rates of work. Janet can complete the task in 9 hours, so her rate of work is 1 task per 9 hours. Similarly, Jancie can complete the task in 10 hours, so her rate of work is 1 task per 10 hours.
To determine how long it will take them to complete the task together, we need to calculate their combined rate of work. This can be done by adding their individual rates:
Combined rate of work = Janet's rate + Jancie's rate
Combined rate of work = 1/9 + 1/10
To calculate this expression, we need to find the least common denominator (LCD) of 9 and 10, which is 90. Multiply each fraction by the appropriate factor to obtain the common denominator:
Combined rate of work = (1/9)*(10/10) + (1/10)*(9/9)
Combined rate of work = 10/90 + 9/90
Combined rate of work = 19/90
Now, we can determine the time it will take them to do the task together by taking the reciprocal of their combined rate:
Time taken together = 1 / Combined rate of work
Time taken together = 1 / (19/90)
Time taken together = 90/19
Therefore, it will take Janet and Jancie approximately 4.74 hours (90/19) to complete the task together.