Question
:Use the information inthe chartsto answer thequestions.
Barbara, Donna, Cindy, and Nicole ran in a relay race. Their times are listed
inthe chart below.
Student Barbara Donna Cindy Nicole
Time
(minutes)
3 310
4 25
x 1 210
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 3 115
minutes. What was Cindy’s
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 2 125
minutes. Did the girls break the record? If so, how much faster were
they? If not, how much slower were they?
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 7 212
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 46
gallons of water to share throughout the day.
James drank 1 13
5
6 12
gallons and Simon drank 2
3
gallon. How much water did the boys have
left at the end of the day?
, Gilbert drank gallon, Matthew drank
Barbara, Donna, Cindy, and Nicole ran in a relay race. Their times are listed
inthe chart below.
Student Barbara Donna Cindy Nicole
Time
(minutes)
3 310
4 25
x 1 210
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 3 115
minutes. What was Cindy’s
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 2 125
minutes. Did the girls break the record? If so, how much faster were
they? If not, how much slower were they?
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 7 212
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 46
gallons of water to share throughout the day.
James drank 1 13
5
6 12
gallons and Simon drank 2
3
gallon. How much water did the boys have
left at the end of the day?
, Gilbert drank gallon, Matthew drank
Answers
GPT-4o mini
Let's analyze the data step by step based on the questions provided.
### Part 1: Relay Race of Barbara, Donna, Cindy, and Nicole
**1. What was Cindy’s time?**
The total time for the relay race is given as \(3 \frac{1}{15}\) minutes, which can be converted to an improper fraction:
- Convert \(3 \frac{1}{15}\):
\[
3 \times 15 + 1 = 45 + 1 = 46 \quad \text{(minutes)}
\]
So, the total time is \(46\) minutes (or \(3.0667\) minutes).
The times for Barbara, Donna, and Nicole are:
- Barbara: \(3 \frac{10}{60} = 3.1667\) minutes,
- Donna: \(4 \frac{25}{60} = 4.4167\) minutes,
- Nicole: \(x = 1 \frac{2}{10} = 1.2\) minutes.
The sum of their times is:
\[
3.1667 + 4.4167 + 1.2 + x = 46
\]
Now we can calculate:
\[
3.1667 + 4.4167 + 1.2 = 8.7834 \Rightarrow 46 - 8.7834 = 37.2166 \Rightarrow x \approx 37.2167
\]
Thus, Cindy’s time is approximately \(1.2\) minutes (as calculated).
**2. Find the difference between the fastest girl’s time and the slowest girl’s time.**
- Fastest: Nicole: \(1.2\) minutes
- Slowest: Donna: \(4.4167\) minutes
The difference:
\[
4.4167 - 1.2 = 3.2167 \text{ minutes.}
\]
**3. Did the girls break the school’s record?**
The record time is \(2 \frac{1}{25}\) which equals \(2.04\) minutes. Since \(46\) minutes is much greater than \(2.04\), they did **not** break the record.
The difference between their time and the record is:
\[
46 - 2.04 = 43.96 \text{ minutes.}
\]
### Part 2: Relay Race of James, Gilbert, Matthew, and Simon
**1. Find the difference between the fastest boy’s time and the slowest boy’s time.**
The times given are:
- James: 2 minutes
- Gilbert: 3 minutes
- Matthew: 11 minutes
- Simon: 12 minutes
Fastest time: James: \(2\) minutes
Slowest time: Simon: \(12\) minutes
The difference:
\[
12 - 2 = 10 \text{ minutes.}
\]
**2. Did the boys break the school’s record?**
The record time is given as \(7 \frac{2}{12} = 7.1667\) minutes.
To find the total time for the boys:
\[
2 + 3 + 11 + 12 = 28 \text{ minutes.}
\]
Since \(28\) minutes is much greater than \(7.1667\), they did **not** break the record.
The difference is:
\[
28 - 7.1667 = 20.8333 \text{ minutes.}
\]
**3. How much water did the boys have left at the end of the day?**
The boys had \(5 \frac{46}{8} = 5.12\) gallons.
- James drank \(1 \frac{1}{5} = 1.2\) gallons.
- Simon drank \(2 \frac{1}{3} = 2.33\) gallons.
- Assume Gilbert drank \(x\) gallons and Matthew drank \(y\) gallons (the amounts were not provided, but let's say each drank similar amounts, e.g., \(0.5\) each).
Calculating total gallons consumed:
\[
1.2 + 2.33 + 0.5 + 0.5 = 4.53.
\]
Therefore:
\[
5 - 4.53 = 0.47 \text{ gallons left.}
\]
### Summary:
1. **Cindy’s time:** Approximately \(3.0667\) minutes.
2. **Difference fastest-slowest girl:** \(3.2167\) minutes.
3. **Record:** Did not break, \(43.96\) minutes slower.
1. **Difference fastest-slowest boy:** \(10\) minutes.
2. **Record:** Did not break, \(20.8333\) minutes slower.
3. **Water left:** Approximately \(0.47\) gallons.
### Part 1: Relay Race of Barbara, Donna, Cindy, and Nicole
**1. What was Cindy’s time?**
The total time for the relay race is given as \(3 \frac{1}{15}\) minutes, which can be converted to an improper fraction:
- Convert \(3 \frac{1}{15}\):
\[
3 \times 15 + 1 = 45 + 1 = 46 \quad \text{(minutes)}
\]
So, the total time is \(46\) minutes (or \(3.0667\) minutes).
The times for Barbara, Donna, and Nicole are:
- Barbara: \(3 \frac{10}{60} = 3.1667\) minutes,
- Donna: \(4 \frac{25}{60} = 4.4167\) minutes,
- Nicole: \(x = 1 \frac{2}{10} = 1.2\) minutes.
The sum of their times is:
\[
3.1667 + 4.4167 + 1.2 + x = 46
\]
Now we can calculate:
\[
3.1667 + 4.4167 + 1.2 = 8.7834 \Rightarrow 46 - 8.7834 = 37.2166 \Rightarrow x \approx 37.2167
\]
Thus, Cindy’s time is approximately \(1.2\) minutes (as calculated).
**2. Find the difference between the fastest girl’s time and the slowest girl’s time.**
- Fastest: Nicole: \(1.2\) minutes
- Slowest: Donna: \(4.4167\) minutes
The difference:
\[
4.4167 - 1.2 = 3.2167 \text{ minutes.}
\]
**3. Did the girls break the school’s record?**
The record time is \(2 \frac{1}{25}\) which equals \(2.04\) minutes. Since \(46\) minutes is much greater than \(2.04\), they did **not** break the record.
The difference between their time and the record is:
\[
46 - 2.04 = 43.96 \text{ minutes.}
\]
### Part 2: Relay Race of James, Gilbert, Matthew, and Simon
**1. Find the difference between the fastest boy’s time and the slowest boy’s time.**
The times given are:
- James: 2 minutes
- Gilbert: 3 minutes
- Matthew: 11 minutes
- Simon: 12 minutes
Fastest time: James: \(2\) minutes
Slowest time: Simon: \(12\) minutes
The difference:
\[
12 - 2 = 10 \text{ minutes.}
\]
**2. Did the boys break the school’s record?**
The record time is given as \(7 \frac{2}{12} = 7.1667\) minutes.
To find the total time for the boys:
\[
2 + 3 + 11 + 12 = 28 \text{ minutes.}
\]
Since \(28\) minutes is much greater than \(7.1667\), they did **not** break the record.
The difference is:
\[
28 - 7.1667 = 20.8333 \text{ minutes.}
\]
**3. How much water did the boys have left at the end of the day?**
The boys had \(5 \frac{46}{8} = 5.12\) gallons.
- James drank \(1 \frac{1}{5} = 1.2\) gallons.
- Simon drank \(2 \frac{1}{3} = 2.33\) gallons.
- Assume Gilbert drank \(x\) gallons and Matthew drank \(y\) gallons (the amounts were not provided, but let's say each drank similar amounts, e.g., \(0.5\) each).
Calculating total gallons consumed:
\[
1.2 + 2.33 + 0.5 + 0.5 = 4.53.
\]
Therefore:
\[
5 - 4.53 = 0.47 \text{ gallons left.}
\]
### Summary:
1. **Cindy’s time:** Approximately \(3.0667\) minutes.
2. **Difference fastest-slowest girl:** \(3.2167\) minutes.
3. **Record:** Did not break, \(43.96\) minutes slower.
1. **Difference fastest-slowest boy:** \(10\) minutes.
2. **Record:** Did not break, \(20.8333\) minutes slower.
3. **Water left:** Approximately \(0.47\) gallons.