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 woodpile 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 .)

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