Solutions

Let t represent the number of minutes Alex needs to peel the potatoes. Tina needs t + 5 minutes to complete the job alone.
Worker
Quantity
Rate
Time
Alex
1
t
Tina
1
t + 5
Together
1
6
The equation to solve is . The LCD is 6 t ( t + 5).
Alex can peel the potatoes in 10 minutes and Tina can peel them in 10 + 5 = 15 minutes.

Let t represent the number of minutes Jared needs to wash the car by himself. The time Rachel needs to wash the car by herself is t + 24.
Worker
Quantity
Rate
Time
Jared
1
t
Rachel
1
t + 24
Together
1
16
The equation to solve is . The LCD is 16 t ( t + 24).
Jared needs 24 minutes to wash the car alone and Rachel needs 24 + 24 = 48 minutes.

Let t represent the number of hours Printing Press II needs to print the run by itself. Because Printing Press I needs five fewer hours than Printing Press II, t – 5 represents the number of hours Printing Press I needs to complete the run by itself.
Worker
Quantity
Rate
Time
Press I
1
t − 5
Press II
1
t
Together
1
6
The equation to solve is . The LCD is 6 t ( t – 5).
Printing Press II can print the run alone in 15 hours and Printing Press I needs 15 – 5 = 10 hours.

Let t represent the number of hours Pipe II needs to fill the reservoir alone. Pipe I needs one hour forty minutes less to do the job, so represents the time Pipe I needs to fill the reservoir by itself.
Worker
Quantity
Rate
Time
Pipe I
1
Pipe II
1
t
Together
1
2
The equation to solve is . The LCD is .
( cannot be a solution because would be negative)
Pipe II can fill the reservoir in 5 hours and Pipe I can fill it in hours or 3 hours 20 minutes.

Let t represent the number of hours Gary needs to unload the truck by himself. John needs 36 minutes more than Gary needs to unload the truck by himself, so John needs more hours or more hours. The number of hours John needs to unload the truck by himself is .
Together they can unload the truck in 1 hour 20 minutes, which is hours. This means that the Together rate is .
Worker
Quantity
Rate
Time
John
1
Gary
1
t
Together
1
The equation to solve is . The LCD is .
Gary needs hours or 2 hours 24 minutes to unload the truck. John needs 2 hours 24 minutes + 36 minutes = 3 hours to unload the truck.
Practice problems for this concept can be found at: Algebra Quadratic Applications Practice Test.
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