Work problems
• #22:
An experienced bricklayer constructs a small
wall in 3 hours. The apprentice (you) completes
the job in 6 hours.
Find how long it takes if they work together.
The answer is not 4.5 hours (no averaging!)
The answer is not 9 hours (Makes no sense!!)
An experienced bricklayer constructs a small wall in 3 hours.
The apprentice (you) completes the job in 6 hours.
Find how long it takes if they work together.
Make a chart!
Hours to complete
total job
Part of job
completed in 1 hr
Experienced worker
3
1/3
You
6
1/6
Team effort
x
1/x
Equation set-up:
1/3 + 1/6 = 1/x
Solution: x = 2 hrs
#21 Section 5.6
• Smith Engineering found that an experienced surveyor surveys a
roadbed in 4 hours. An apprentice surveyor needs 5 hours to do the
job. If the two work together, find how long it takes them to
complete the job?
How long to finish
the job
Portion of the job
completed in 1 hr.
Co-worker
4 hrs
¼
Apprentice
5 hrs
1/5
X
1/x
Team or working
together
• Set-up:
• 1/4 + 1/5 = 1/x
LCD = 20x
Solution x = 20/9 hours
#26: Distance = Rate X Time
• A boat can travel 9 miles upstream in the
same amount of time it takes to travel 11
miles downstream. If the current of the river is
3 mi/hr, complete the chart below and use it
to find the speed of the boat in still water.
A boat can travel 9 miles upstream in the same amount of time it takes to travel 11
miles downstream. If the current of the river is 3 mi/hr, complete the chart below and
use it to find the speed of the boat in still water (let boat speed = x).
Dist = rate x time 
time = Dist/rate
Distance
Rate (boat & river)
Time
Upstream (against
river current –
slows you down)
9 mi
X-3
(Same time)
Downstream (with
river current –
speeds you up)
11 mi
X+3
(Same time)
Set-up:
9

11
9(x+3) = 11 (x-3)
9x+27 = 11x-33
27+33 = 11x – 9x
60
= 2x
30
= x
The speed of the boat in still water is 30 mi/hr
x3
x3