Work Rate Problems in Mathematics

This video tutorial covers solving work and time problems using algebraic formulas. It begins with an introduction to the concept and a simple formula for calculating the time taken by individuals or groups to complete tasks. The video includes several example problems involving different numbers of people working together or individually, demonstrating how to apply the formula and solve for unknown variables. Each problem is explained step-by-step, with emphasis on finding the least common multiple and using algebraic manipulation to find solutions.

If John can paint a room in 6 hours and Sally in 3 hours, how long will it take them to paint the room together?

• 2 hours

• 1 hour

• 4 hours

• 3 hours

Mark and Kelly can finish a job in 4 hours together. If Mark takes 6 hours alone, how long does Kelly take alone?

• 10 hours

• 12 hours

• 8 hours

• 14 hours

Alex, Kristen, and Ronald can complete a task in 6, 9, and 18 hours respectively. How long will it take them to finish the task together?

• 2 hours

• 3 hours

• 5 hours

• 4 hours

If Stephanie can finish a job in 8 hours and Megan in 24 hours, how long will it take Luke to finish the job alone if all three can do it in 4 hours together?

• 10 hours

• 12 hours

• 14 hours

• 16 hours

If Greg can do a job four times faster than Aya, and together they can do it in 4 hours, how long does it take Greg alone?

• 5 hours

• 8 hours

• 6 hours

• 7 hours

Lisa can do a job three times faster than Tom, and Karen twice as fast as Tom. If all three can build a treehouse in 2 hours, how long does it take Karen alone?

• 6 hours

• 7 hours

• 4 hours

• 5 hours

If Aya takes 20 hours to complete a job alone, how long does it take Greg if he is four times faster?

• 6 hours

• 4 hours

• 5 hours

• 7 hours

Ashley and Ricky can complete a job in 7.2 hours, Ricky and Andrew in 12 hours, and Ashley and Andrew in 9 hours. How long will it take all three to complete the job together?

• 5 hours

• 6 hours

• 8 hours

• 7 hours

If Ashley and Ricky can complete a job in 7.2 hours, how long does it take Ashley alone if Ricky takes 12 hours?

• 13 hours

• 12 hours

• 11 hours

• 10 hours

If Andrew can do a job in 9 hours and Ashley in 7.2 hours, how long does it take Ricky alone if all three can do it in 6 hours?

• 13 hours

• 10 hours

• 12 hours

• 11 hours