50+ Time Word Problems worksheets for 6th Grade on Quizizz | Free ... - Free Printable

Problem Analysis and Solutions

The problems provided involve finding the Least Common Multiple (LCM) and the Greatest Common Factor (GCF) in various real-world scenarios. Let's solve each problem step by step.

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#### Problem 1:
Question: The school cafeteria serves tacos every sixth day and cheeseburgers every eighth day. If tacos and cheeseburgers are both on today's menu, how many days will it be before they are both on the menu again?

- Key Concept: We need to find the Least Common Multiple (LCM) of 6 and 8 because we are looking for the smallest number of days after which both events (serving tacos and cheeseburgers) coincide again.

- Steps:
1. Prime factorization:
- \( 6 = 2 \times 3 \)
- \( 8 = 2^3 \)
2. To find the LCM, take the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \) (from 8).
- For \( 3 \): The highest power is \( 3^1 \) (from 6).
3. Multiply these together:
\[
\text{LCM}(6, 8) = 2^3 \times 3 = 8 \times 3 = 24
\]

- Answer: The next time tacos and cheeseburgers will both be on the menu is in 24 days.

- Correct Option: D. 24 days

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#### Problem 2:
Question: A radio station is giving away a $100 bill to every 30th caller and movie tickets to every 40th caller. Which caller will be the first to win both prizes?

- Key Concept: We need to find the Least Common Multiple (LCM) of 30 and 40 because we are looking for the smallest caller number that is a multiple of both 30 and 40.

- Steps:
1. Prime factorization:
- \( 30 = 2 \times 3 \times 5 \)
- \( 40 = 2^3 \times 5 \)
2. To find the LCM, take the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^3 \) (from 40).
- For \( 3 \): The highest power is \( 3^1 \) (from 30).
- For \( 5 \): The highest power is \( 5^1 \) (from both 30 and 40).
3. Multiply these together:
\[
\text{LCM}(30, 40) = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120
\]

- Answer: The first caller to win both prizes will be the 120th caller.

- Correct Option: C. 120

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#### Problem 3:
Question: Two clocks are turned on at the same time. One clock chimes every 15 minutes, and the other clock chimes every 25 minutes. In how many minutes will they chime together?

- Key Concept: We need to find the Least Common Multiple (LCM) of 15 and 25 because we are looking for the smallest time interval after which both clocks chime together.

- Steps:
1. Prime factorization:
- \( 15 = 3 \times 5 \)
- \( 25 = 5^2 \)
2. To find the LCM, take the highest power of each prime factor:
- For \( 3 \): The highest power is \( 3^1 \) (from 15).
- For \( 5 \): The highest power is \( 5^2 \) (from 25).
3. Multiply these together:
\[
\text{LCM}(15, 25) = 3 \times 5^2 = 3 \times 25 = 75
\]

- Answer: The clocks will chime together after 75 minutes.

- Correct Option: A. 75 minutes

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#### Problem 4:
Question: Henry and Margo both began traveling around a circular track. Henry is riding his bike, and Margo is walking. It takes Henry 7 minutes to make it all the way around, and Margo takes 12 minutes. How much time will pass until they meet at the starting line?

- Key Concept: We need to find the Least Common Multiple (LCM) of 7 and 12 because we are looking for the smallest time interval after which both Henry and Margo complete an integer number of laps and return to the starting line simultaneously.

- Steps:
1. Prime factorization:
- \( 7 = 7 \) (prime)
- \( 12 = 2^2 \times 3 \)
2. To find the LCM, take the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^2 \) (from 12).
- For \( 3 \): The highest power is \( 3^1 \) (from 12).
- For \( 7 \): The highest power is \( 7^1 \) (from 7).
3. Multiply these together:
\[
\text{LCM}(7, 12) = 2^2 \times 3 \times 7 = 4 \times 3 \times 7 = 84
\]

- Answer: Henry and Margo will meet at the starting line after 84 minutes.

- Correct Option: D. 84 minutes

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#### Problem 5:
Question: Jenny goes to karate class every 12 days and to the library every 18 days. On December 1st she went to both class and the library. On what date will she do both class and go to the library?

- Key Concept: We need to find the Least Common Multiple (LCM) of 12 and 18 because we are looking for the smallest number of days after which both events (going to karate class and the library) coincide again.

- Steps:
1. Prime factorization:
- \( 12 = 2^2 \times 3 \)
- \( 18 = 2 \times 3^2 \)
2. To find the LCM, take the highest power of each prime factor:
- For \( 2 \): The highest power is \( 2^2 \) (from 12).
- For \( 3 \): The highest power is \( 3^2 \) (from 18).
3. Multiply these together:
\[
\text{LCM}(12, 18) = 2^2 \times 3^2 = 4 \times 9 = 36
\]

- Answer: Jenny will go to both karate class and the library again in 36 days. Since she went on December 1st, the next date will be January 6th.

- Correct Option: B. 36 days

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Final Answers:

1. D. 24 days
2. C. 120
3. A. 75 minutes
4. D. 84 minutes
5. B. 36 days

\boxed{D, C, A, D, B}