Michael and Barry can complete a job in 2 hours when working together. If Michael requires 6 hours to do the job alone, how many days does Barry need to do the job alone?
2=1/(1/6+1/B)
=>
B=1/(1/2-1/6)=3
Well, if Michael takes 6 hours to do the job alone, we can safely assume he's not running for Employee of the Month anytime soon. Now, let's see how efficiently Barry works. If they can complete the job together in 2 hours, it means they do 1/2 of the job in that time. Since we all know Michael can do the job alone in 6 hours, that means he does 1/6 of the job in one hour.
Now, let's get Barry in the spotlight. If they do 1/2 of the job together in 2 hours, then Barry must also do 1/2 of the job in 2 hours. But we're trying to find how many days Barry needs to do the job alone, so we need to convert that.
If Barry takes 2 hours to do 1/2 of the job, it means he takes 4 hours to do the whole job alone. And since there are 24 hours in a day (last time I checked), we can divide that by Barry's 4 hours.
So, it looks like Barry needs 6 whole days to complete the job on his own. Looks like he's got a lot of free time on his hands!
To find out how many days Barry needs to do the job alone, we can start by determining their individual work rates.
Let's assume that the job is completed in 1 hour when Barry works alone. Therefore, we can determine Michael's work rate by considering the amount of work he can do in 1 hour. Since Michael requires 6 hours to do the job alone, his work rate is 1/6 of the job per hour.
Their combined work rate is 1/2 of the job per hour, which means that if they work together, they can complete half of the job in 1 hour.
Now, let's find Barry's work rate by subtracting Michael's work rate from their combined work rate:
1/2 (combined work rate) - 1/6 (Michael's work rate) = 1/3 (Barry's work rate)
This means that Barry can complete 1/3 of the job per hour when working alone.
Since we're trying to determine how many days Barry needs to complete the job, we need to convert the hours to days.
Given that there are 24 hours in a day, we can calculate how many days Barry needs by dividing 1 hour by his work rate and then converting it to days:
1 / (1/3) = 3
So, Barry needs 3 days to complete the job alone.
To solve this problem, we need to use the concept of "work rates." We can think of work rates as the fraction of the job that a person can complete in one hour.
Let's assign the work rate of Michael as M (fraction of the job he can complete in one hour) and the work rate of Barry as B (fraction of the job he can complete in one hour).
If Michael and Barry can complete the job together in 2 hours, this means that their combined work rate is 1/2 (since they complete half of the job in one hour together).
So we have the equation: M + B = 1/2
If Michael requires 6 hours to do the job alone, this means that his work rate is 1/6 (since he completes 1/6 of the job in one hour).
So we have the equation: M = 1/6
We can substitute this value of M into the first equation:
1/6 + B = 1/2
Now we can solve for B:
B = 1/2 - 1/6
To subtract fractions, we need a common denominator, which in this case is 6:
B = 3/6 - 1/6
B = 2/6
Simplifying the fraction, we get:
B = 1/3
Now we have found that Barry's work rate is 1/3, which means he can complete 1/3 of the job in one hour.
To find out how many days Barry would need to do the job alone, we need to determine how many hours are in a day. Let's assume there are 24 hours in a day.
Since Barry can complete 1/3 of the job in one hour, he would need 3 hours to complete the whole job.
Now, if there are 24 hours in a day, we can divide the total number of hours Barry needs (3 hours) by 24 hours to find how many days he needs:
3 hours / 24 hours = 1/8
So Barry needs 1/8 of a day to do the job alone, which is equivalent to approximately 0.125 days.
Therefore, Barry would need approximately 0.125 days to complete the job alone.