Question
Fractions at the Finish Line
Directions: Use the information in the charts to answer the questions.
Barbara, Donna, Cindy, and Nicole ran in a relay race. Their times are listed
in the chart below.
Student Barbara Donna Cindy Nicole
Time
(minutes)
3
3
10
2
4
5
x 1
2
10
1. The four girls ran in a relay race as a team. Each girl ran one part of
the race. The team’s total time was 3
11
minutes. What was Cindy’s
5
time?
2. Find the difference between the fastest girl’s time and the slowest
girl’s time.
3. To break the school’s record, the girls’ time had to be faster than 2
12
5
minutes. Did the girls break the record? If so, how much faster were
they? If not, how much slower were they?
© 2017 Connections Education LLC. All rights reserved.
James, Gilbert, Matthew, and Simon ran in a relay race. Their times are
listed in the chart below.
Student James Gilbert Matthew Simon
Time
(minutes)
2
3
11
12
5
6
7
12
1. Find the difference between the fastest boy’s time and the slowest
boy’s time.
2. To break the school’s record, the boys’ time had to be faster than 7
2
12
minutes. Estimate to decide if the boys broke the record. If so, how
much faster were they? If not, how much slower were they?
3. The boys had 5
4
6 gallons of water to share throughout the day.
James drank 1
1
5
3
, Gilbert drank gallon, Matthew drank 1
6 1
2
gallons and Simon drank 2
3 gallon. How much water did the boys have
left at the end of the day?
Directions: Use the information in the charts to answer the questions.
Barbara, Donna, Cindy, and Nicole ran in a relay race. Their times are listed
in the chart below.
Student Barbara Donna Cindy Nicole
Time
(minutes)
3
3
10
2
4
5
x 1
2
10
1. The four girls ran in a relay race as a team. Each girl ran one part of
the race. The team’s total time was 3
11
minutes. What was Cindy’s
5
time?
2. Find the difference between the fastest girl’s time and the slowest
girl’s time.
3. To break the school’s record, the girls’ time had to be faster than 2
12
5
minutes. Did the girls break the record? If so, how much faster were
they? If not, how much slower were they?
© 2017 Connections Education LLC. All rights reserved.
James, Gilbert, Matthew, and Simon ran in a relay race. Their times are
listed in the chart below.
Student James Gilbert Matthew Simon
Time
(minutes)
2
3
11
12
5
6
7
12
1. Find the difference between the fastest boy’s time and the slowest
boy’s time.
2. To break the school’s record, the boys’ time had to be faster than 7
2
12
minutes. Estimate to decide if the boys broke the record. If so, how
much faster were they? If not, how much slower were they?
3. The boys had 5
4
6 gallons of water to share throughout the day.
James drank 1
1
5
3
, Gilbert drank gallon, Matthew drank 1
6 1
2
gallons and Simon drank 2
3 gallon. How much water did the boys have
left at the end of the day?
Answers
Answered by
GPT-4o mini
Let's go through the questions step-by-step.
### For the Girls' Relay Race:
1. **Finding Cindy's Time:**
The total time for the team was \(3 \frac{11}{5}\) minutes, which can be converted into an improper fraction:
\[
3 \frac{11}{5} = \frac{15}{5} + \frac{11}{5} = \frac{26}{5} \text{ minutes}
\]
The team times for Barbara, Donna, and Nicole are given as follows:
- Barbara: \(3 \frac{2}{10} = 3.2 = \frac{16}{5}\) minutes
- Donna: \(4 \frac{5}{10} = 4.5 = \frac{9}{2} = \frac{18}{4} = \frac{36}{10} = \frac{18}{4}\) minutes
- Nicole: \(5 \frac{1}{10} = 5.1 = \frac{51}{10}\) minutes
Adding these together and setting it equal to the total gives:
\[
\text{Cindy's Time} = \frac{26}{5} - \left(\frac{16}{5} + \frac{9}{2} + \frac{51}{10}\right)
\]
We need a common denominator to combine the times. The least common denominator for 5, 2, and 10 is 10.
- Convert all fractions to have a denominator of 10:
- Barbara: \(\frac{16}{5} = \frac{32}{10}\)
- Donna: \(\frac{9}{2} = \frac{45}{10}\)
- Nicole: \(\frac{51}{10}\) is already in the correct form.
Now, add Barbara, Donna, and Nicole's times:
\[
\text{Sum} = \frac{32}{10} + \frac{45}{10} + \frac{51}{10} = \frac{128}{10}
\]
Then, subtract from the total time:
\[
\text{Cindy's Time} = \frac{26}{5} - \frac{128}{10} = \frac{52}{10} - \frac{128}{10} = \frac{-76}{10} = -7.6 \text{ minutes}
\]
Since this doesn't make sense, there must be an error in the numbers. Let's assume Cindy's time is not one of the initial three, meaning we might just need the collective team time and so forth.
2. **Finding the Difference Between the Fastest and Slowest:**
Assuming the times are:
- Fastest: Barbara (3.2)
- Slowest: Cindy (10)
The difference:
\[
10 - 3.2 = 6.8 \text{ minutes}
\]
3. **Breaking the Record:**
The record is \(2 \frac{5}{12}\) minutes:
Converting \(2 \frac{5}{12}\):
\[
2 \frac{5}{12} = \frac{29}{12} \text{ minutes}
\]
Since \(3 \frac{11}{5}\) is more than \(2 \frac{5}{12}\), they did **not** break the record. Calculating the difference:
\[
\frac{26}{5} - \frac{29}{12}
\]
Using a common denominator (60):
\[
\frac{312}{60} - \frac{145}{60} = \frac{167}{60} = 2.7833 \text{ minutes}
\]
### For the Boys' Relay Race:
1. **Finding the Difference Between Fastest and Slowest:**
The times are:
- Fastest: James (2)
- Slowest: Matthew (12)
The difference:
\[
12 - 2 = 10 \text{ minutes}
\]
2. **Breaking the Record:**
The record is \(7 \frac{2}{12}\):
Converting \(7 \frac{2}{12}\):
\[
7 \frac{1}{6} = \frac{43}{6} \text{ minutes}
\]
Checking the team:
James: 2, Gilbert: 3, Matthew: 11, Simon: 12.
Total Time:
\[
2 + 3 + 11 + 12 = 28 \text{ minutes}
\]
Since 28 is greater than 43/6, they did not break the record; the difference can be calculated by converting both to common denominators, or approximating.
3. **Water Calculations:**
The total water \(5 \frac{4}{6}\) = \(5 + 0.67 = 5.667 \text{ gallons}\):
Consumption:
James: \(1 \frac{1}{5} = 1.2\),
Gilbert: \(\frac{7}{2} = 3.5\),
Matthew: \(1.6\),
Simon: \(2\).
Adding total consumption:
\[
= 1.2 + 3.5 + 1.6 + 2 = 8.3 \text{ gallons consumed}
\]
All calculations should be checked and aligned according to total consumption remaining. Careful thought on each value is recommended.
### For the Girls' Relay Race:
1. **Finding Cindy's Time:**
The total time for the team was \(3 \frac{11}{5}\) minutes, which can be converted into an improper fraction:
\[
3 \frac{11}{5} = \frac{15}{5} + \frac{11}{5} = \frac{26}{5} \text{ minutes}
\]
The team times for Barbara, Donna, and Nicole are given as follows:
- Barbara: \(3 \frac{2}{10} = 3.2 = \frac{16}{5}\) minutes
- Donna: \(4 \frac{5}{10} = 4.5 = \frac{9}{2} = \frac{18}{4} = \frac{36}{10} = \frac{18}{4}\) minutes
- Nicole: \(5 \frac{1}{10} = 5.1 = \frac{51}{10}\) minutes
Adding these together and setting it equal to the total gives:
\[
\text{Cindy's Time} = \frac{26}{5} - \left(\frac{16}{5} + \frac{9}{2} + \frac{51}{10}\right)
\]
We need a common denominator to combine the times. The least common denominator for 5, 2, and 10 is 10.
- Convert all fractions to have a denominator of 10:
- Barbara: \(\frac{16}{5} = \frac{32}{10}\)
- Donna: \(\frac{9}{2} = \frac{45}{10}\)
- Nicole: \(\frac{51}{10}\) is already in the correct form.
Now, add Barbara, Donna, and Nicole's times:
\[
\text{Sum} = \frac{32}{10} + \frac{45}{10} + \frac{51}{10} = \frac{128}{10}
\]
Then, subtract from the total time:
\[
\text{Cindy's Time} = \frac{26}{5} - \frac{128}{10} = \frac{52}{10} - \frac{128}{10} = \frac{-76}{10} = -7.6 \text{ minutes}
\]
Since this doesn't make sense, there must be an error in the numbers. Let's assume Cindy's time is not one of the initial three, meaning we might just need the collective team time and so forth.
2. **Finding the Difference Between the Fastest and Slowest:**
Assuming the times are:
- Fastest: Barbara (3.2)
- Slowest: Cindy (10)
The difference:
\[
10 - 3.2 = 6.8 \text{ minutes}
\]
3. **Breaking the Record:**
The record is \(2 \frac{5}{12}\) minutes:
Converting \(2 \frac{5}{12}\):
\[
2 \frac{5}{12} = \frac{29}{12} \text{ minutes}
\]
Since \(3 \frac{11}{5}\) is more than \(2 \frac{5}{12}\), they did **not** break the record. Calculating the difference:
\[
\frac{26}{5} - \frac{29}{12}
\]
Using a common denominator (60):
\[
\frac{312}{60} - \frac{145}{60} = \frac{167}{60} = 2.7833 \text{ minutes}
\]
### For the Boys' Relay Race:
1. **Finding the Difference Between Fastest and Slowest:**
The times are:
- Fastest: James (2)
- Slowest: Matthew (12)
The difference:
\[
12 - 2 = 10 \text{ minutes}
\]
2. **Breaking the Record:**
The record is \(7 \frac{2}{12}\):
Converting \(7 \frac{2}{12}\):
\[
7 \frac{1}{6} = \frac{43}{6} \text{ minutes}
\]
Checking the team:
James: 2, Gilbert: 3, Matthew: 11, Simon: 12.
Total Time:
\[
2 + 3 + 11 + 12 = 28 \text{ minutes}
\]
Since 28 is greater than 43/6, they did not break the record; the difference can be calculated by converting both to common denominators, or approximating.
3. **Water Calculations:**
The total water \(5 \frac{4}{6}\) = \(5 + 0.67 = 5.667 \text{ gallons}\):
Consumption:
James: \(1 \frac{1}{5} = 1.2\),
Gilbert: \(\frac{7}{2} = 3.5\),
Matthew: \(1.6\),
Simon: \(2\).
Adding total consumption:
\[
= 1.2 + 3.5 + 1.6 + 2 = 8.3 \text{ gallons consumed}
\]
All calculations should be checked and aligned according to total consumption remaining. Careful thought on each value is recommended.