Work (shared work) problem (Algebra 1/2)

One type of word problem dealing with number of hours worked by x number of workers typically trips up a lot of student.  Students get overwhelmed by this type of word problem because they just don't know how to setup this kind of problem.  This article hopefully will help you solve some of that mystery.

Example1:  It takes Tom and Jerry 3 hours to construct a woodshed together.  If Tom can construct the woodshed in 4 hours by himself, how long will it take Jerry to construct the same woodshed by himself?

Let x = number of hours it will take Jerry to construct the woodshed  by himself
Let 1 = total work done to construct one woodshed

Then

1/4 = The fraction of work that Tom can construct per hour by himself
1/x = The fraction of work that Jerry can construct per hour by himself
1/3 = The fraction of work that Tom & Jerry combined can construct per hour

Therefore

1/4 + 1/x = 1/3
x/4x + 4/4x = 1/3
(x + 4)/4x = 1/3
4x = 3(x + 4)
4x = 3x + 12
x = 12

So Jerry can construct the woodshed by himself in 12 hours.

Example 2:  It takes 1 painter 12 hours to paint an entire house, while it takes another painter 8 hours to take the same house.  How long will it take both painters to paint this same house?

Painter 1:  the amount of work accomplished per hour is 1/12
Painter 2:  the amount of work accomplished per hour is 1/8

When working together, painter 1 and 2 in 1 hour can do

1/12 + 1/8 = 2/24 + 3/24 = 5/24 of work

Let x = number of hours it take for both painters to work together

1/x = the amount of work accomplished by both painters per hour

So

1/x = 5/24

Solving for x, we get x = 24/5, x = 4 4/5 hour = 4 hour 48 min.

If you have any question regarding this type of problems, please feel free to reach out to me or any of the instructors in my center.

Michael Huang
Mathnasium of Glen Rock/Ridgewood
236 Rock Road
Glen Rock, NJ 07452
Tel:  201-444-8020
glenrock@mathnasium.com