Combine work rates

Add the work completed per hour to find a shared finishing time.

Count work done in one hour

A and B each finish one job alone in 4 hours. Both work at steady rates without slowing each other down.

Each completes 1/4 job per hour. Together: 1/4 + 1/4 = 1/2 job per hour. One job takes 1 ÷ (1/2) = 2 hours.

In 1 hA: 4 h1/4B: 4 h1/41/4 + 1/4 = 1/21 ÷ (1/2) = 2 h
Filled parts show the work done in one hour.

Combine unequal rates

A finishes one job alone in 3 hours; B takes 6 hours. They work together at steady rates without slowing each other down.

Their rates add: 1/3 + 1/6 = 1/2 job per hour. One job takes 1 ÷ (1/2) = 2 hours.

In 1 hA: 3 h1/3B: 6 h1/61/3 + 1/6 = 1/21 ÷ (1/2) = 2 h
Add fractions of the same whole job.

Try two equal workers

A and B each take 6 hours to finish one job alone. They start together and work at steady rates without slowing each other down.

Find each worker’s fraction of a job per hour. Add the rates, then divide one whole job by that total.

In 1 hA: 6 h1/6B: 6 h1/6A + B? h
Each bar represents one complete job.

Try it

A and B each need 6 hours alone. At steady rates without slowing each other down, how long do they need together for one job?

  1. 3 h
  2. 12 h
Show the answer

3 h

Yes. 1/6 + 1/6 = 1/3 job per hour. One job takes 1 ÷ (1/3) = 3 hours.

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