Work Problems Practice Problems
Set 1: Work Problems - Two Works Working at Different Rates
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Practice
- Sherry and Denise together can mow a yard in 20 minutes. Alone, Denise can mow the yard in 30 minutes. How long would Sherry need to mow the yard by herself?
- Together, Ben and Brandon can split a pile of wood in 2 hours. If Ben could split the same pile of wood in 3 hours, how long would it take Brandon to split the pile alone?
- A boy can weed the family garden in 90 minutes. His sister can weed it in 60 minutes. How long will they need to weed the garden if they work together?
- Robert needs 40 minutes to assemble a bookcase. Paul needs 20 minutes to assemble the same bookcase. How long will it take them to assemble the bookcase if they work together?
- Together, two pipes can fill a reservoir in
of an hour. Pipe I needs one hour ten minutes ( 
hours) to fill the reservoir by itself. How long would Pipe II need to fill the reservoir by itself? - A pipe can drain a reservoir in 6 hours 30 minutes (
hours). A larger pipe can drain the same reservoir in 4 hours 20 minute ( 
hours). How long will it take to drain the reservoir if both pipes are used?
Solutions
In the following, t will represent the unknown time.
-
Worker
Quantity
Rate
Time
Sherry
1
1/ t
t
Denise
1
1/30
30
Together
1
1/20
20
The equation to solve is 1/ t + 1/30 = 1/20. The LCD is 60 t .
Alone, Sherry can mow the yard in 60 minutes.
-
Worker
Quantity
Rate
Time
Ben
1
1/3
3
Brandon
1
1/ t
t
Together
1
1/2
2
The equation to solve is 1/3 + 1/ t = 1/2. The LCD is 6 t .
Brandon can split the wood-pile by himself in 6 hours.
-
Worker
Quantity
Rate
Time
Boy
1
1/90
90
Girl
1
1/60
60
Together
1
1/ t
t
The equation to solve is 1/90 + 1/60 = 1/ t . The LCD is 180 t .
Working together, the boy and girl need 36 minutes to weed the garden.
-
Worker
Quantity
Rate
Time
Robert
1
1/40
40
Paul
1
1/20
20
Together
1
1/ t
t
The equation to solve is 1/40 + 1/20 = 1/ t . The LCD is 40 t .
Together Robert and Paul can assemble the bookcase in
minutes or 13 minutes 20 seconds. -
Worker
Quantity
Rate
Time
Pipe I
1
6/7
7/6
Pipe II
1
1/ t
t
Together
1
3/4
The equation to solve is 6/7 + 1/ t = 4/3. The LCD is 21 t .
Alone, Pipe II can fill the reservoir in
hours or 2 hours, 6 minutes. ( 
of an hour is of 60 minutes and 
.) -
Worker
Quantity
Rate
Time
Pipe I
1
Pipe I
1
Together
1
1/ t
t
The equation to solve is 2/13 + 3/13 = 1/ t . The LCD is 13 t .
Together the pipes can drain the reservoir in
hours or 2 hours 36 minutes. ( 
of hour is of 60 minutes and 
.)
of the job, so 
of the job remains. Let t represent the number of minutes both hoses will be used.
minutes or 6 minutes 40 seconds. Therefore, Hose 1 will be used for 
of the job, so 
of the job remains to be done.
hours or 16 hours 40 minutes ( 
of an hour is 
of 60 minutes— 
hours or 15 hours 20 minutes to complete the run.-
1
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