Hours needed

Question

A mason can build a wall in 6 hours less than an apprentice. Together they can build a wall in 4 hours. How long would it take the apprentice working alone to build the wall?

Answer 1

Let's say that 

M = # hours it takes the Mason to build the wall.

A = # hours it takes the Apprentice to build the wall.

 

We know that M = A - 6

 

We also know that 

 

1/M + 1/A = 1/4, where 4 = number of hours to build the wall when the mason and apprentice work together.

Substituting M = A-6 in the equation above, we have

1/(A-6) + 1/A = 1/4

 

Rearranging terms we have,

1 + (A-6)/A = (A-6)/4

A + (A-6) = A(A-6)/4

4A + 4(A-6) = A(A-6)

4A + 4A - 24 = A² - 6A

8A - 24 = A² - 6A

and

0 = A² -14A + 24

 

We can factor and solve

0= (A-8) (A-6)

 

Setting each factor equal to 0 and solving

A= 8 or A = 6

 

We can discard the A=6 solution because if A=6, then M=0 and this is an illogical solution since the mason cannot build a wall in 0 hours.

 

But when A = 8, then M = 2.

 

So it would take the apprentice 8 hours working alone to build the wall.

 

Hope this helps.