Ann, Matt and Zack are working for a cleaning company. Together, they can clean a house in 2 hours. If Ann does the job alone she can finish it in 5 hours. If Matt does the job alone he can finish it in 6 hours.
How long will it take Ann and Zack together to finish the job?
1/a + 1/m + 1/z = 1/2
so,
1/5 + 1/6 + 1/z = 1/2
1/z = 2/15
1/a + 1/z = 1/5 + 2/15 = 1/3
so, Ann and Zack take 3 hours to do the job together.
Well, it's no clean joke, but we'll solve this together!
If Ann and Matt working together can clean a house in 2 hours, then in one hour they can complete 1/2 of the job.
We know that Ann alone can finish the job in 5 hours, which means she can complete 1/5 of the job in one hour.
Similarly, Matt alone can finish the job in 6 hours, so he can complete 1/6 of the job in one hour.
Let's call the amount of the job that Zack can complete in one hour "Z".
So, putting it all together, we have the equation:
1/5 + 1/6 + Z = 1/2
Now, if we solve for Z:
1/5 + 1/6 + Z = 1/2
(6 + 5)/30 + Z = 15/30
11/30 + Z = 15/30
Z = 15/30 - 11/30
Z = 4/30
Z = 2/15
Therefore, Zack alone can complete 2/15 of the job in one hour.
So, it will take Ann and Zack working together to complete the job:
1 / (1/5 + 2/15)
To simplify, we'll do some math acrobatics:
1 / (3/15 + 2/15)
1 / (5/15)
1 / (1/3)
3
So, it will take Ann and Zack working together 3 hours to finish the job. Have a sparkling good time cleaning!
First, let's find out how much of the job each person can do per hour.
Ann can complete 1/5 of the job in one hour (since she can finish the job alone in 5 hours).
Matt can complete 1/6 of the job in one hour (since he can finish the job alone in 6 hours).
Together, Ann and Matt can complete 1/2 of the job in one hour (since they can finish the job together in 2 hours).
Now, let's find out how much of the job Zack can do per hour when working with Ann.
Since Ann and Matt combined can finish 1/2 of the job in one hour, and we know that Ann can complete 1/5 of the job in one hour, we can subtract 1/5 from 1/2 to find out how much Zack can do in one hour.
1/2 - 1/5 = 5/10 - 2/10 = 3/10
This means that Zack can complete 3/10 of the job in one hour when working with Ann.
Finally, to find out how long it will take Ann and Zack together to finish the job, we invert the fraction, so we have:
10/3 = 3.33
Therefore, Ann and Zack together will take approximately 3.33 hours to finish the job.
To find out how long it will take Ann and Zack together to finish the job, we can first determine Ann's and Zack's individual rates of work, and then add their rates to find their combined rate.
We can calculate Ann's rate of work by considering the inverse of her completion time. If Ann completes the job alone in 5 hours, her rate of work is 1 house per 5 hours, or 1/5 houses per hour.
Similarly, we can calculate Zack's rate of work as the inverse of his completion time. If Zack completes the job with the combined efforts of Ann and Matt in 2 hours, his rate of work is 1 house per 2 hours, or 1/2 houses per hour.
To find the combined rate of Ann and Zack working together, we add their individual rates: 1/5 + 1/2 = 2/10 + 5/10 = 7/10 houses per hour.
Now that we know the combined rate, we can calculate the time it will take Ann and Zack together to finish the job by finding the reciprocal of their combined rate. Dividing 1 by 7/10 gives us approximately 1.43.
Therefore, it will take Ann and Zack approximately 1.43 hours, or 1 hour and 26 minutes, to finish the job together.