Find the time for two people working together to complete a task if it takes them 4.5 hrs and 6 hrs working individually.
1/x = 1/4.5 + 1/6
Solve that for x. The answer wil be in hours.
This assumes they work indepently on the same job. If they help each other and each does what he or she is best at, it might go faster. If they get in each other's way and fight, it will take longer.
To find the time it takes for two people working together to complete a task, you can use the concept of work rates.
Let's label the work rate of the first person as W1, and the work rate of the second person as W2. The work rate is the amount of work done per unit of time.
We can determine the work rate of each person by considering the time it takes for them to complete the task individually.
For the first person, it takes 6 hours to complete the task individually. So, the work rate of the first person is W1 = 1 task / 6 hours.
Similarly, for the second person, it takes 4.5 hours to complete the task individually. So, the work rate of the second person is W2 = 1 task / 4.5 hours.
Now that we have the work rates of both individuals, we can calculate their combined work rate when working together. The combined work rate is simply the sum of their individual work rates: W_combined = W1 + W2.
W_combined = 1/6 + 1/4.5
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 9.
W_combined = 1/6 + 2/9
To add the fractions, we need to have the same denominator, so we can multiply the first fraction by 3/3:
W_combined = 3/18 + 2/9
W_combined = 3/18 + 4/18
W_combined = 7/18
This means that when the two people work together, their combined work rate is 7/18 tasks per hour.
Finally, to find the time it takes for the two people to complete the task together, we can use the formula:
Time = 1 / W_combined
Time = 1 / (7/18)
Time = 18/7 hours
Therefore, when the two people work together, it takes them approximately 2.57 hours (or 2 hours and 34 minutes) to complete the task.