Question

Russell 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

Answer:

32 hours.

Step-by-step explanation:

Let x represent the time taken by Russell and Aaron to build the shed.

We have been given that Russell and Aaron can build a shed in 8 hours when working together. Aaron works three times as fast as Russel.

Russell's work rate would be $\frac{1}{x}$.

Since Aaron works three times as fast as Russel, so Aaron's work rate would be $\frac{3}{x}$.

Part of work done by in one hour would be $\frac{1}{8}$.

We can represent our given information in an equation as:

$\frac{1}{x}+\frac{3}{x}=\frac{1}{8}$

Let us solve for x.

$\frac{1}{x}*8x+\frac{3}{x}*8x=\frac{1}{8}*8x$

$8+3*8=x$

$8+24=x$

$32=x$

Therefore, it will take Russell 32 hours to build the shed working alone.