Algebra Puzzle – Challenge 44

A perfect mathematics challenge to tease your brain and check your critical and creative thinking skills!

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

The Absolute Best Book to challenge your Smart Student!

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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