Question

Ben takes 2 days to write 5 reports, while Kate takes 3 days to write 5 reports. How much greater is Ben's rate, in reports per day, compared to Kate's rate?

a) 5/2
b) 5/3
c) 5/4
d) 5/6

Answer 1

To determine how much greater Ben's rate is compared to Kate's, we find the rates of both in reports per day and subtract them. Ben's rate is 5/2 reports per day, and Kate's rate is 5/3 reports per day. The difference in their rates is 5/6 reports per day, making option d) the correct answer.

Step-by-step explanation:

We need to calculate Ben's and Kate's rates and find the difference between them. Ben's rate is 5 reports in 2 days, which is 5/2 reports per day. Kate's rate is 5 reports in 3 days, which is 5/3 reports per day.

To find out how much greater Ben's rate is compared to Kate's, we subtract Kate's rate from Ben's rate:

Ben's rate - Kate's rate = (5/2) - (5/3)

To perform this subtraction, we need a common denominator, which is 6 in this case. Hence, we convert:

(5/2)*(3/3) - (5/3)*(2/2) = (15/6) - (10/6)

Now, subtract the numerators to find the difference:

15/6 - 10/6 = 5/6

Therefore, Ben's rate is 5/6 reports per day greater than Kate's rate.