Question

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?

Answer 1

32 hours

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