A word problem involving separate time for each party when you know how long it takes them together.

Question

a baker works 4 times as fast as his assistant the total time to finish a project is 36 minutes. if they both worked separately how long would it take each of them?

Answer 1

Hi Courtney,

 

From what I understand, we need to set up an equation such as the following one:

 

4x + x = 36 (minutes)

 

4x represents the baker - we use 4x because the baker works 4 times as fast

 

x represents the assistant - we use x because the assistant works 4 times slower, thus resulting in 4x/4 = x

 

From the equation, 4x + x = 36, we combine like-terms to get 5x = 36.

 

Next, we solve for x by dividing each side of the equals sign by 5 (basic algebra).

 

This results in an x value of 7.2 (minutes).

 

We are not done though!

 

We need to substitute 7.2 back into the original equation to solve for total time of baker 4(7.2) = 28.8 minutes

 

and 1(7.2) = 7.2 minutes.

 

We can check our answer by adding 4(7.2) and 1(7.2) to get 36 minutes.

 

Our correct amount of time between the two (the baker and the assistant).