Identify these questions

Rate of work questions are increasingly being tested and these types of questions look like this:

If Steve can paint a fence in 30 hours and Elizabeth can paint the same fence in 15 hours, how long will it take for both of them to paint the fence together?

To identify them, look for questions that usually have a request to find:

• A time period for two or more people working together on a project.
• The time that one person works on a project.
• How much has passed in terms of task completion in a particular time.
• The number of participants required if the time period or task has changed.

Now that we know what these questions look like, let’s see how we can answer them.

The strategy to answer these questions

To answer these questions the same rules apply in dealing with worded questions and for these questions, the main rule is that you want to reduce it down to a rate of 1 unit – why? Because… then you can calculate any ups or downs easily.

Here’s the general process:

• Find the requirement
• Express the information in a common basic unit – this could be a time period or a participant, or a task.
• Express the rate of time as a fraction of a whole.
• If working together, add the fractions together to get a combined rate of time.
• Divide the fraction by a whole to get the time period.

Let’s see this process applied to the questions below.

Example Question/s

Watch video for explanation of the following question/s:

If Steve can paint a fence in 30 hours and Elizabeth can paint the same fence in 15 hours, how long will it take for both of them to paint the fence together?

A 7.5 hours

B 10 hours

C 15 hours

D 25 hours

If it takes 500 people 20 days to dig a 500-metre hole, how many people are required to dig the same hole in 5 days?

A 1,000

B 2,000

C 5,000

D 10,000

Key Rules to remember

• Find the requirement
• Express the information in a common basic unit – this could be a time period or a participant, or a task.
• Express the rate of time as a fraction of a whole.
• If working together, add the fractions together to get a combined rate of time.
• Divide the fraction by a whole to get the time period.

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let's get started on your practice questions.

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