The first constructor can build the room in_____days. The second constructor can build the room in_____days.

Question

Two constructors working together finished building a room in 6 days. How long would it take for each constructor to build the room by himself, if it is known that one of them would require 9 more days than the other?

Answer 1

Marvin,

This is a bit tricky, so concentrate.

Let x = number of days  it takes first guy by himself

Let x + 9 = number of days it takes slower guy by himself.

Look at the rate they work.  In one day, the first guy does 1/x of the job.  The second guy, in one day, does 1/(x+9) of the job.  So those are their daily rates.  The problem states that in 6 days, they finish the job.  Then each day they do a fractional part of the job, and together, they finish the one job. Re-read this until it makes sense.

days * rate + days*rate = 1 job completed

6 (1/x) + 6 (1/(x+9) ) =1 

6/x + 6/(x+9) = 1

Next we want to clear the fractions.  We multiply both sides by

(x) (x + 9).  This is messy and you have to be careful.

(x) (x+9) (6/x) + (x) (x+9) (6/(x+9) = 1 (x) (x+9)

6(x+9) + 6x = x² +9x

6x + 54 +6x = x² + 9x

12x +54 = x² + 9x

0 = x² -3x -54

Now you have a nice quadratic equation.  Factor and solve.  Throw away the negative number.  You now have the number of days it takes the faster guy by himself. Substitute the solution into the original definition of terms, and you will get the number of days it takes each one by himself.

Wasn't that fun?  Or at least interesting....

Mary