Combined Rate Calculations - CCAT Test Prep

This type of question tests your understanding of combining rates of different workers or machines working together. It is often seen in production or efficiency-related scenarios where you need to determine how long it will take to complete a task if multiple people or machines are working simultaneously.

combined-rate

How to Solve Combined Rate Problems Step-by-Step

Question 1 - Combined Assembly Rates

A manufacturing company has two assembly lines, one with old equipment and one with new. The old assembly line generates products at a rate of 48 per hour, the new one at 60 per hour. If both assembly lines are operating at the same time, how long will it take them to create a total of 180 products?

  • A) 1 hour and 20 minutes
  • B) 1 hour and 24 minutes
  • C) 1 hour and 30 minutes
  • D) 1 hour and 36 minutes
  • E) 1 hour and 40 minutes

Understand the Problem:

You have two assembly lines:

  • Old equipment: 48 products per hour
  • New equipment: 60 products per hour
  • You need to determine the total time required for them to assemble 180 products.

Calculate the Combined Rate:

Step 1: Add Their Rates

Combined rate  
   = 48 + 60  
   = 108 products per hour

Step 2: Find Out How Long It Takes

Since the combined rate is 108 products per hour, and you need to produce 180 products, we can determine the time:

Time required  
   = Total products / Combined rate  
   = 180 / 108 hours  
   = 1 hour and 40 minutes

Answer: 1 hour and 40 minutes

Question 2 - Combined Efforts for a Goal

Two carpenters are working together to build chairs. Carpenter A can build 5 chairs per hour, and Carpenter B can build 7 chairs per hour. How long will it take both of them to build a total of 60 chairs?

  • A) 3 hours and 30 minutes
  • B) 4 hours and 15 minutes
  • C) 4 hours and 45 minutes
  • D) 5 hours and 10 minutes
  • E) 5 hours and 20 minutes

Calculate the Combined Rate:

Combined rate  
   = 5 + 7  
   = 12 chairs per hour

Now, we need to calculate the time required to make 60 chairs.

Time required  
   = 60 / 12 hours  
   = 5 hours

Answer: 5 hours

Question 3 - Combined Rates in Different Units

Two painters are painting a wall. Painter A can paint at a rate of 20 square meters per hour, while Painter B paints at 30 square meters per hour. How long will it take them to paint a wall of 250 square meters if they work 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

Calculate the Combined Rate:

Combined rate  
   = 20 + 30  
   = 50 square meters per hour

Time required  
   = 250 / 50 hours  
   = 5 hours

Answer: 5 hours

How to Solve These Questions in Your Head

  1. Combine the Rates: Simply add the rates together to get the combined rate.
  2. Divide Total Task by Combined Rate: Divide the total number of products or amount of work by the combined rate to get the time required.
  3. Convert Decimal Hours to Hours and Minutes: If the result is not a whole number, convert the decimal portion into minutes to get an exact answer.

By breaking down the calculation into simple steps and using addition and division, you can solve these combined rate problems quickly.

20 Practice Questions - Combined Rate Problems

  1. Two workers can paint a house together. Worker A paints at 5 square meters per hour, Worker B at 3 square meters per hour. How long will it take to paint 64 square meters?

    • A) 5 hours
    • B) 6 hours and 20 minutes
    • C) 8 hours
    • D) 8 hours and 45 minutes
    • E) 10 hours

  2. Two machines produce gadgets, one at 20 gadgets per hour and the other at 15 gadgets per hour. How long will it take them together to produce 210 gadgets?

    • A) 6 hours and 20 minutes
    • B) 7 hours
    • C) 8 hours
    • D) 10 hours
    • E) 12 hours

  3. Two plumbers working together can fix 15 pipes per hour. Plumber A fixes 9 pipes per hour. How many hours will it take them together to fix 90 pipes?

    • A) 4 hours
    • B) 5 hours
    • C) 6 hours
    • D) 7 hours
    • E) 8 hours

  4. A car factory has two production lines. One makes 30 cars per day, and the other makes 45 cars per day. How long will it take them together to make 300 cars?

    • A) 4 days
    • B) 5 days
    • C) 6 days and 16 hours
    • D) 7 days
    • E) 8 days

  5. Worker A can lay bricks at 40 bricks per hour, and Worker B at 30 bricks per hour. If they work together, how long will it take to lay 280 bricks?

    • A) 2 hours
    • B) 3 hours and 15 minutes
    • C) 4 hours
    • D) 5 hours
    • E) 6 hours

  6. Two conveyor belts move boxes, one at 25 boxes per hour and the other at 35 boxes per hour. How long will it take to move 360 boxes?

    • A) 4 hours and 48 minutes
    • B) 5 hours and 30 minutes
    • C) 6 hours
    • D) 7 hours
    • E) 8 hours

  7. Assembly Line A makes 40 parts per hour, and Assembly Line B makes 60 parts per hour. How long will it take both lines to make 500 parts?

    • A) 3 hours and 15 minutes
    • B) 4 hours
    • C) 4 hours and 45 minutes
    • D) 5 hours
    • E) 6 hours

  8. Two delivery trucks deliver at 20 packages per hour and 25 packages per hour respectively. How long will it take them to deliver 360 packages?

    • A) 6 hours
    • B) 7 hours and 20 minutes
    • C) 8 hours
    • D) 9 hours and 15 minutes
    • E) 10 hours

  9. A construction site has two cement mixers, one at 15 cubic meters per hour and the other at 10 cubic meters per hour. How long will it take to mix 100 cubic meters of cement?

    • A) 4 hours and 30 minutes
    • B) 5 hours and 15 minutes
    • C) 6 hours and 40 minutes
    • D) 7 hours
    • E) 8 hours

  10. Workers A and B together complete a task at a combined rate of 90 units per day. Worker A alone completes 40 units per day. How long will it take them to complete 450 units?

    • A) 3 days and 8 hours
    • B) 4 days
    • C) 5 days
    • D) 5 days and 10 hours
    • E) 6 days

  11. Two chefs can bake 80 cakes per day together. Chef A bakes 30 cakes per day. How long will it take both chefs to bake 400 cakes?

    • A) 3 days
    • B) 4 days
    • C) 5 days
    • D) 6 days
    • E) 7 days

  12. Painter A can paint 25 square meters per hour, and Painter B paints 35 square meters per hour. Together, how long will it take to paint 450 square meters?

    • A) 5 hours
    • B) 6 hours
    • C) 7 hours and 15 minutes
    • D) 8 hours
    • E) 9 hours

  13. A manufacturing facility has two machines, producing at 12 units per hour and 18 units per hour respectively. How long will it take them to produce 270 units?

    • A) 6 hours
    • B) 7 hours and 20 minutes
    • C) 8 hours
    • D) 9 hours
    • E) 10 hours

  14. Two janitors can clean an office building. Janitor A can clean at 200 square meters per hour, and Janitor B at 300 square meters per hour. How long will it take to clean 5000 square meters?

    • A) 8 hours
    • B) 9 hours
    • C) 10 hours
    • D) 11 hours
    • E) 12 hours

  15. Two operators are assembling parts. Operator A can assemble 15 parts per hour, while Operator B can assemble 20 parts per hour. How long will it take to assemble 140 parts?

    • A) 3 hours and 10 minutes
    • B) 4 hours
    • C) 4 hours and 30 minutes
    • D) 5 hours
    • E) 6 hours

  16. Line A packages 30 boxes per hour, while Line B packages 50 boxes per hour. How long will it take to package 320 boxes?

    • A) 3 hours
    • B) 4 hours
    • C) 5 hours and 10 minutes
    • D) 6 hours
    • E) 7 hours

  17. Workers A and B work on constructing a road. Worker A constructs 10 meters per hour, and Worker B 15 meters per hour. How long will it take to construct 250 meters?

    • A) 8 hours
    • B) 9 hours and 30 minutes
    • C) 10 hours
    • D) 12 hours
    • E) 15 hours

  18. A garage has two mechanics working together to repair cars. One repairs 3 cars per day, while the other repairs 5 cars per day. How long will it take them to repair 64 cars?

    • A) 7 days
    • B) 8 days
    • C) 9 days
    • D) 10 days
    • E) 11 days

  19. Two musicians play at 30 songs per hour and 40 songs per hour respectively. How long will it take to play 280 songs?

    • A) 3 hours
    • B) 4 hours and 30 minutes
    • C) 5 hours
    • D) 6 hours
    • E) 7 hours

  20. Two machines work together to label bottles. Machine A can label 100 bottles per hour, and Machine B labels 150 bottles per hour. How long will it take to label 1200 bottles?

    • A) 3 hours and 45 minutes
    • B) 4 hours
    • C) 4 hours and 30 minutes
    • D) 5 hours
    • E) 6 hours

Answers

  1. Combined rate = 5 + 3 = 8 square meters per hour.
    • Time required = 64 / 8 = 8 hours.
    • Answer: C) 8 hours
  2. Combined rate = 20 + 15 = 35 gadgets per hour.
    • Time required = 210 / 35 = 6 hours.
    • Answer: A) 6 hours and 20 minutes
  3. Combined rate = 15 pipes per hour.
    • Time required = 90 / 15 = 6 hours.
    • Answer: C) 6 hours
  4. Combined rate = 30 + 45 = 75 cars per day.
    • Time required = 300 / 75 = 4 days.
    • Answer: A) 4 days
  5. Combined rate = 40 + 30 = 70 bricks per hour.
    • Time required = 280 / 70 = 4 hours.
    • Answer: C) 4 hours
  6. Combined rate = 25 + 35 = 60 boxes per hour.
    • Time required = 360 / 60 = 6 hours.
    • Answer: C) 6 hours
  7. Combined rate = 40 + 60 = 100 parts per hour.
    • Time required = 500 / 100 = 5 hours.
    • Answer: D) 5 hours
  8. Combined rate = 20 + 25 = 45 packages per hour.
    • Time required = 360 / 45 = 8 hours.
    • Answer: C) 8 hours
  9. Combined rate = 15 + 10 = 25 cubic meters per hour.
    • Time required = 100 / 25 = 4 hours.
    • Answer: A) 4 hours and 30 minutes
  10. Combined rate = 90 units per day.
    • Time required = 450 / 90 = 5 days.
    • Answer: C) 5 days
  11. Combined rate = 80 cakes per day.
    • Time required = 400 / 80 = 5 days.
    • Answer: C) 5 days
  12. Combined rate = 25 + 35 = 60 square meters per hour.
    • Time required = 450 / 60 = 7.5 hours.
    • Answer: C) 7 hours and 15 minutes
  13. Combined rate = 12 + 18 = 30 units per hour.
    • Time required = 270 / 30 = 9 hours.
    • Answer: D) 9 hours
  14. Combined rate = 200 + 300 = 500 square meters per hour.
    • Time required = 5000 / 500 = 10 hours.
    • Answer: C) 10 hours
  15. Combined rate = 15 + 20 = 35 parts per hour.
    • Time required = 140 / 35 = 4 hours.
    • Answer: B) 4 hours
  16. Combined rate = 30 + 50 = 80 boxes per hour.
    • Time required = 320 / 80 = 4 hours.
    • Answer: B) 4 hours
  17. Combined rate = 10 + 15 = 25 meters per hour.
    • Time required = 250 / 25 = 10 hours.
    • Answer: C) 10 hours
  18. Combined rate = 3 + 5 = 8 cars per day.
    • Time required = 64 / 8 = 8 days.
    • Answer: B) 8 days
  19. Combined rate = 30 + 40 = 70 songs per hour.
    • Time required = 280 / 70 = 4 hours.
    • Answer: B) 4 hours and 30 minutes
  20. Combined rate = 100 + 150 = 250 bottles per hour.
    • Time required = 1200 / 250 = 4.8 hours.
    • Answer: C) 4 hours and 30 minutes
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