Question

A baker can decorate the days cookie supply four times as fast as his new assistant, if they decorate all the cookies working together in 32 minutes, how long would it take for each of them to decorate the cookies working individually?

Answer 1

Given:

• Number of minutes they spent decorating together = 32 minutes.

,

• Baker A can decorate four times as fast as his new assistant.

Let's find the number of minutes it will take for each of them to decorate the cookies working individually.

Let x represent the number of minutes it will take the new assistant.

Let y represent the number of minutes it will take the baker.

Let the jobe be completed = 1

We have:

• y = 4x

,

• 32/x + 32/y = 1

Solve the system using substitution method.

Substitute 4x for y in equation 2.

We have the equation:

`(32)/(x)+(32)/(4x)=1`

•

Let's solve the equation for x:

`\begin{gathered} (32)/(x)*4x+(32)/(4x)*4x=1*4x \\ \\ 4(32)+32=4x \\ \\ 128+32=4x \\ \\ 160=4x \end{gathered}`

Solving further:

Divide both sides by 4

`\begin{gathered} (160)/(4)=(4x)/(4) \\ \\ 40=x \\ \\ x=40 \end{gathered}`

Substitute 40 for x in y = 4x

`\begin{gathered} y=4x \\ \\ y=4(40) \\ \\ y=160 \end{gathered}`

Therefore, we have the solution:

x = 40, y = 160

Therefore, it will take 40 minutes for the baker to decorate while it will take 160 minutes for his assistant.

ANSWER:

It will take 40 minutes for the baker to decorate while it will take 160 minutes for his assistant.