Work Rate Calculations - CCAT Test Prep

This type of question tests your understanding of combined work rates, where you determine how quickly two workers or machines, each with different productivity rates, can complete a task together. This method is helpful in planning tasks and estimating project durations. The solution uses straightforward arithmetic to keep calculations simple and understandable.

How to Solve Combined Work Rate Problems Step-by-Step

Question 1 - Work Rate Calculation

If one worker can assemble 9 products per hour, and another worker can assemble 6 products per hour, how long will it take them to assemble a total of 50 products if they both start working at the same time?

A) 2 hours and 40 minutes
B) 2 hours and 45 minutes
C) 3 hours and 15 minutes
D) 3 hours and 20 minutes
E) 4 hours and 10 minutes

Find the Combined Work Rate

Worker 1 assembles 9 products per hour.
Worker 2 assembles 6 products per hour.

Combined rate:

Combined rate 
    = 9 + 6 
    = 15 products per hour

Determine Total Time Needed

We need to assemble a total of 50 products.

Using the combined rate:

Total time (in hours) 
    = 50 / 15 
    = 3.333 hours

Convert the Time into Hours and Minutes

3.333 hours is equal to 3 hours and 20 minutes (since 0.333 hours is approximately 20 minutes).

Answer: 3 hours and 20 minutes

Question 2 - Combined Work Rate

If one machine can produce 8 items per hour, and another machine can produce 12 items per hour, how long will it take them to produce 100 items if both work together?

A) 4 hours and 10 minutes
B) 5 hours
C) 5 hours and 30 minutes
D) 6 hours
E) 7 hours

Calculate the Combined Production Rate

Machine 1: 8 items per hour
Machine 2: 12 items per hour

Combined rate 
    = 8 + 12 
    = 20 items per hour

Calculate the Time Needed

To produce 100 items:

Total time (in hours) 
    = 100 / 20 
    = 5 hours

Answer: 5 hours

Question 3 - Teamwork Productivity

One worker can paint 5 walls per hour, while another worker can paint 7 walls per hour. How many hours will it take for them to paint 48 walls if they start at the same time?

A) 3 hours and 30 minutes
B) 4 hours
C) 4 hours and 15 minutes
D) 5 hours
E) 5 hours and 30 minutes

Find the Combined Painting Rate

Worker 1: 5 walls per hour
Worker 2: 7 walls per hour

Combined rate 
    = 5 + 7 
    = 12 walls per hour

Calculate the Time Needed

To paint 48 walls:

Total time (in hours) 
    = 48 / 12 
    = 4 hours

Answer: 4 hours

How to Solve These Questions Easily

Add the Rates Together

Determine how much work both workers or machines can complete in an hour by adding their rates.

Divide the Total Task by Combined Rate

Use the total number of items or tasks and divide by the combined rate to determine how much time is needed.

Convert Hours to Minutes

If needed, convert any fractional hours into minutes for a more precise answer.

By following these steps, you can solve combined work rate problems with ease.

20 Practice Questions - Work Rate Calculations

One worker can produce 10 units per hour, and another can produce 15 units per hour. How long will it take them to produce 75 units if they work together?

A) 2 hours and 30 minutes
B) 3 hours
C) 3 hours and 15 minutes
D) 3 hours and 30 minutes
E) 4 hours

One person can fill 5 bottles per hour, and another can fill 8 bottles per hour. How long will it take them to fill 65 bottles if they work together?

A) 5 hours and 10 minutes
B) 6 hours
C) 6 hours and 30 minutes
D) 7 hours
E) 7 hours and 15 minutes

One carpenter can make 7 chairs per hour, and another can make 5 chairs per hour. How many hours will it take them to make 72 chairs together?

A) 5 hours
B) 5 hours and 30 minutes
C) 6 hours
D) 6 hours and 15 minutes
E) 7 hours

One painter can paint 4 rooms per hour, while another can paint 6 rooms per hour. How long will it take them to paint 50 rooms together?

A) 4 hours and 45 minutes
B) 5 hours
C) 5 hours and 30 minutes
D) 6 hours
E) 6 hours and 15 minutes

A machine produces 20 items per hour, and another produces 10 items per hour. How long will it take them to produce 150 items together?

A) 4 hours and 30 minutes
B) 5 hours
C) 5 hours and 15 minutes
D) 5 hours and 45 minutes
E) 6 hours

One person types 45 words per minute, while another types 30 words per minute. How long will it take them to type 9,000 words together?

A) 2 hours
B) 2 hours and 20 minutes
C) 2 hours and 30 minutes
D) 2 hours and 45 minutes
E) 3 hours

One machine can produce 25 widgets per hour, and another can produce 15 widgets per hour. How long will it take them to produce 200 widgets together?

A) 4 hours and 10 minutes
B) 4 hours and 30 minutes
C) 5 hours
D) 5 hours and 20 minutes
E) 6 hours

One worker assembles 10 parts per hour, and another assembles 12 parts per hour. How long will it take them to assemble 88 parts if they work together?

A) 3 hours
B) 3 hours and 30 minutes
C) 4 hours
D) 4 hours and 10 minutes
E) 5 hours

One baker bakes 15 loaves of bread per hour, while another bakes 10 loaves per hour. How long will it take them to bake 150 loaves together?

A) 5 hours
B) 5 hours and 10 minutes
C) 5 hours and 30 minutes
D) 6 hours
E) 6 hours and 15 minutes

One person can complete 6 tasks per hour, and another can complete 9 tasks per hour. How long will it take them to complete 90 tasks if they work together?

A) 5 hours
B) 5 hours and 30 minutes
C) 6 hours
D) 6 hours and 15 minutes
E) 7 hours

One worker builds 8 tables per hour, while another builds 12 tables per hour. How long will it take them to build 80 tables together?

A) 3 hours
B) 3 hours and 45 minutes
C) 4 hours
D) 4 hours and 30 minutes
E) 5 hours

One gardener plants 5 trees per hour, and another plants 10 trees per hour. How long will it take them to plant 90 trees together?

A) 4 hours
B) 4 hours and 30 minutes
C) 5 hours
D) 5 hours and 20 minutes
E) 6 hours

One cleaner cleans 7 rooms per hour, while another cleans 8 rooms per hour. How long will it take them to clean 75 rooms together?

A) 4 hours and 10 minutes
B) 4 hours and 30 minutes
C) 5 hours
D) 5 hours and 30 minutes
E) 6 hours

One mechanic fixes 5 cars per hour, and another fixes 7 cars per hour. How long will it take them to fix 60 cars together?

A) 4 hours
B) 4 hours and 20 minutes
C) 5 hours
D) 5 hours and 40 minutes
E) 6 hours

One plumber repairs 8 pipes per hour, while another repairs 6 pipes per hour. How long will it take them to repair 70 pipes together?

A) 3 hours and 30 minutes
B) 4 hours
C) 4 hours and 15 minutes
D) 4 hours and 30 minutes
E) 5 hours

One machine produces 18 products per hour, while another produces 12 products per hour. How long will it take them to produce 150 products together?

A) 4 hours
B) 4 hours and 10 minutes
C) 5 hours
D) 5 hours and 30 minutes
E) 6 hours

One worker paints 8 walls per hour, and another paints 9 walls per hour. How long will it take them to paint 102 walls together?

A) 5 hours
B) 5 hours and 15 minutes
C) 5 hours and 30 minutes
D) 6 hours
E) 6 hours and 20 minutes

One person finishes 4 reports per hour, and another person finishes 6 reports per hour. How long will it take them to finish 90 reports together?

A) 7 hours
B) 7 hours and 30 minutes
C) 8 hours
D) 8 hours and 15 minutes
E) 9 hours

One chef cooks 10 meals per hour, while another cooks 15 meals per hour. How long will it take them to cook 200 meals together?

A) 5 hours
B) 6 hours
C) 6 hours and 20 minutes
D) 7 hours
E) 8 hours

One machine can produce 22 parts per hour, and another machine can produce 18 parts per hour. How long will it take them to produce 160 parts together?

A) 3 hours
B) 3 hours and 45 minutes
C) 4 hours
D) 4 hours and 20 minutes
E) 5 hours

Answers

B) 3 hours
B) 6 hours
C) 6 hours
B) 5 hours
B) 5 hours
C) 2 hours and 30 minutes
C) 5 hours
B) 3 hours and 30 minutes
A) 5 hours
B) 5 hours and 30 minutes
C) 4 hours
B) 4 hours and 30 minutes
D) 5 hours and 30 minutes
B) 4 hours and 20 minutes
D) 4 hours and 30 minutes
C) 5 hours
B) 5 hours and 15 minutes
A) 7 hours
B) 6 hours
C) 4 hours

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