Maria, an experienced shipping clerk, can fill a certain order in 8 hours.Felipe, a new clerk, needs 9 hours to do the same job. Working together, how long will it take them to fill the order?
To solve this problem, we can use the concept of work rates.
Maria's work rate is 1/8 of the job per hour, while Felipe's work rate is 1/9 of the job per hour.
When they work together, their work rates add up. So, the combined work rate is 1/8 + 1/9 = (9 + 8)/(8 * 9) = 17/72 of the job per hour.
Therefore, working together, they can fill the entire order in 72/17 hours, which is approximately 4.24 hours.
To find out how long it will take Maria and Felipe to fill the order together, we can use the formula:
\(\frac{1}{\text{Time taken by Maria}} + \frac{1}{\text{Time taken by Felipe}} = \frac{1}{\text{Time taken together}}\)
Substituting the given values into the formula:
\(\frac{1}{8} + \frac{1}{9} = \frac{1}{\text{Time taken together}}\)
Now, we can solve for the time taken together by simplifying the equation:
\(\frac{9 + 8}{72} = \frac{1}{\text{Time taken together}}\)
\(\frac{17}{72} = \frac{1}{\text{Time taken together}}\)
To isolate the time taken together, we can take the reciprocal of both sides of the equation:
\(\text{Time taken together} = \frac{72}{17}\)
Now, we can calculate the time taken together:
\(\text{Time taken together} \approx 4.24\) hours
Therefore, it will take Maria and Felipe approximately 4.24 hours to fill the order together.
To find out how long it will take Maria and Felipe to fill the order when working together, we need to calculate their combined work rate.
Maria takes 8 hours to complete the job, which means she can do 1/8th of the job per hour (1 job / 8 hours = 1/8 job per hour). Felipe takes 9 hours to complete the job, so he can do 1/9th of the job per hour (1 job / 9 hours = 1/9 job per hour).
To find out their combined work rate, we add their individual rates together:
1/8 job per hour + 1/9 job per hour = (9/72) + (8/72) = 17/72 job per hour.
Now, to find out how long it will take them to complete the job together, we divide the job by their combined work rate:
1 job / (17/72 job per hour) = 72/17 hours.
Therefore, it will take Maria and Felipe approximately 4.24 hours (or about 4 hours and 14 minutes) to fill the order when working together.