Russel and Aaron can build a shed in 8 hours when working together. Aaron works three times as fast as Russel. How long would it take Russel to build the shed if he were to work alone?

Question

Mathematics

Mariam

18 January, 02:36

Russel and Aaron can build a shed in 8 hours when working together. Aaron works three times as fast as Russel. How long would it take Russel to build the shed if he were to work alone?

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Answers (1)

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Allie Henry · Answer 1

32 hours

Step-by-step explanation:

Let's assume they are to build a certain volume say X.

Now their rate when working together would be X/8

Let the time taken for Aaron be y. Since he works 3 times as fast as Russel, the time taken by Russel will be 3y.

Hence, Aaron's rate would be X/y and Russel's X/3y

This means:

x/8 = x/y + x/3y

1/8 = 1/y + 1/3y

1/8 = 4/3y

3y = 32

y = 32/3 = 10hrs. 40 minutes.

Now Russel's time is 3 * 10hrs 40 minutes = 32hours