Alma can grade a batch of placement exams in 3hr and Kevin can grade a batch in 4hr. if they work together to grade a batch of exams, what percentage of the exams will have been graded by Alma?
Assuming they both work the same time, Alma works 4/3 as fast as Kevin, so she does 4/7 of the work, or 57%
Or, you can find how long it takes to do the whole job together:
1/x = 1/4 + 1/3
x = 12/7
So, in 12/7 hours, Alma does 1/3 * 12/7 = 4/7 of the work.
To find the percentage of exams that will have been graded by Alma, we need to calculate the ratio of the time it takes Alma to grade exams compared to the total time it takes both Alma and Kevin to grade exams.
Let's assume that the batch of exams consists of 100 exams (although the actual number of exams is not provided in the question, this assumption will simplify the explanation).
First, find the amount of work done by Alma and Kevin individually:
- Alma can grade a batch of exams in 3 hours, so she can grade 100 exams in 3 hours.
- Kevin can grade a batch of exams in 4 hours, so he can grade 100 exams in 4 hours.
Now, let's find the total time it takes both of them to grade the exams together:
Alma takes 3 hours to grade 100 exams, and Kevin takes 4 hours to grade 100 exams. Therefore, in 1 hour, Alma can grade 100/3 exams and Kevin can grade 100/4 exams.
To find the amount of work Alma and Kevin do in 1 hour, we add their rates of work together:
Alma's rate = 100/3 exams per hour
Kevin's rate = 100/4 exams per hour
Total rate = 100/3 + 100/4 exams per hour
To simplify the calculation, we find a common denominator:
Total rate = 400/12 + 300/12 exams per hour
Total rate = 700/12 exams per hour
Now we have the combined rate at which Alma and Kevin can grade exams.
To find the percentage of exams graded by Alma, we divide Alma's rate by the total rate and multiply by 100:
Percentage of exams graded by Alma = (Alma's rate / Total rate) * 100
Substituting the values:
Percentage of exams graded by Alma = (100/3) / (700/12) * 100
Simplifying further:
Percentage of exams graded by Alma = (100/3) * (12/700) * 100
Performing the calculations:
Percentage of exams graded by Alma ≈ 20.57%
Therefore, approximately 20.57% of the exams will have been graded by Alma.