Algebra Puzzle – Challenge 44

Challenge:

Edward can finish \(40\%\) of a job in 2 days and Emanuel can finish \(15\%\) of the same job in 3 days. How many days does it take Edward and Emanuel to finish \(75\%\) of the same job if they work together?

A- 2.5

B- 3

C- 4.5

D- 5

E- 5.5

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Edward can finish \(40\%\) of a job in 2 days. Therefore, he can finish the job in 5 days.
\(40\%\) of x = 2 → x = 5
Emanuel can finish \(15\%\) of the same job in 3 days. So, he can finish the whole job in 20 days.
\(15\%\) of x = 3 → x = 20
First, let’s find the time it takes to finish the job if both Edward and Emanuel work together.
\(\frac{1}{a} + \frac{1}{b} = \frac{1}{t} → \frac{1}{5} + \frac{1}{20} = \frac{1}{t} →\frac{5}{20} = \frac{1}{t} → t = 4\)
It takes 4 days to finish the job if both of them work together. Therefore, they can finish \(75\%\) of the job in 3 days:
\(x = 4 → 75\%\) of x equals 3.

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