Find the time for two people working together to complete half a task if it takes them 8 hours and 10 hours to complete the entire task working individually.
rate of worker 1 = job/8
rate of worker 2 = job/10
their combined rate = job/8 + job/10
= (4job + 5job)/140 = 9job/40
so the time is job/(9job/40) = 4.44 hours
or 4 hours and 27 minutes
(job canceled in the division of fractions above)
Thank you so much Reiny=:)
To find the time it takes for two people to complete half a task, we can use the concept of "work rates."
First, let's find the work rates of each person. If one person can complete the entire task alone in 8 hours, their work rate is 1/8 of the task per hour. Similarly, if the other person can complete the entire task alone in 10 hours, their work rate is 1/10 of the task per hour.
Now, let's determine their combined work rate when working together. Since they are working simultaneously, we can add their individual work rates together. So, the combined work rate is (1/8 + 1/10) of the task per hour.
To find the time it takes for them to complete half the task, we can set up the equation:
(1/8 + 1/10) * t = 1/2
where 't' represents the time in hours.
Now, let's solve the equation:
(18/80) * t = 1/2
By multiplying both sides by 80/18, we get:
t = (1/2) * (80/18)
Simplifying this expression, we find:
t = 40/18
Reducing the fraction gives:
t ≈ 2.22 hours
Therefore, it will take approximately 2.22 hours for two people working together to complete half the task.