Martha can rake the leaves in her yard in 2 hours. Her brother can do the job in 8 hours. How long will it take them to do the job working together?
Together, in an hour, they do (1/2+1/8)=5/8 of the job.
So they will finish the job in (8/5)=1 3/8 hours = 1h22.5 min.
Emily can rake her lawn in 5 hours. Andrew can rake the same lawn in 8 hours. Rounded to the nearest hour, how long will the job take if they work together?
To find the time it will take Martha and her brother to rake the leaves together, we can use the concept of "work rates."
Let's say Martha's work rate is R_m (the amount of work she can do in one hour), and her brother's work rate is R_b.
The work rate is calculated by dividing the amount of work done by the time taken. In this case, we can assume that the amount of work is the same (raking the leaves in the yard).
Work rate of Martha (R_m) = 1 yard / 2 hours = 1/2 yards per hour
Work rate of brother (R_b) = 1 yard / 8 hours = 1/8 yards per hour
To find the combined work rate of Martha and her brother, we can add their individual work rates:
Combined work rate = R_m + R_b
= 1/2 + 1/8
= 4/8 + 1/8
= 5/8 yards per hour
Now, let's use the combined work rate to find the time it will take both of them to rake the leaves together.
Time taken = Total work / combined work rate
= 1 yard / (5/8 yards per hour)
= 1 yard * (8/5) hours
= 8/5 hours
= 1 hour 36 minutes
Therefore, it will take Martha and her brother 1 hour 36 minutes to rake the leaves together.
To solve this problem, we can use the concept of work rates. The work rate is a measure of how much work a person can do in a given unit of time.
Let's start by calculating Martha's work rate. We are given that Martha can rake the leaves in her yard in 2 hours, so her work rate would be 1 job/2 hours, or 1/2 job per hour.
Similarly, we can calculate Martha's brother's work rate. We are told that he can do the job in 8 hours, so his work rate would be 1 job/8 hours, or 1/8 job per hour.
Now, to find the time it would take them to complete the job together, we need to add up their individual work rates and find the reciprocal of the sum.
Martha's work rate + Brother's work rate = (1/2) + (1/8) = 4/8 + 1/8 = 5/8 job per hour.
To find the time it would take them to finish the job together, we can take the reciprocal of their combined work rate:
1 / (5/8) = 8/5 = 1.6 hours.
Therefore, it would take Martha and her brother 1.6 hours, or 1 hour and 36 minutes, to complete the job together.