Question
Dylan is swimming laps to practice for a swim meet. One lap is 25 yards. He swims in 10-minute intervals at a rate of 100 yards per 1.85 minutes. Dylan completes 40 strokes each minute.
emphasis,Part A,end emphasis,
Which proportion could be solved to determine the number of laps Dylan swims in 10 minutes?
Question 1 Answer options with 4 options
A.
StartFraction 1.85 over 4 EndFraction equals StartFraction 10 over x EndFraction
B.
StartFraction 1.85 over 25 EndFraction equals StartFraction 10 over x EndFraction
C.
StartFraction 1.85 over 40 EndFraction equals StartFraction 10 over x EndFraction
D.
StartFraction 1.85 over 100 EndFraction equals StartFraction 10 over x EndFraction
emphasis,Part B,end emphasis,
How many complete laps does Dylan swim in 170 strokes? Enter the answer in the box.
emphasis,Part A,end emphasis,
Which proportion could be solved to determine the number of laps Dylan swims in 10 minutes?
Question 1 Answer options with 4 options
A.
StartFraction 1.85 over 4 EndFraction equals StartFraction 10 over x EndFraction
B.
StartFraction 1.85 over 25 EndFraction equals StartFraction 10 over x EndFraction
C.
StartFraction 1.85 over 40 EndFraction equals StartFraction 10 over x EndFraction
D.
StartFraction 1.85 over 100 EndFraction equals StartFraction 10 over x EndFraction
emphasis,Part B,end emphasis,
How many complete laps does Dylan swim in 170 strokes? Enter the answer in the box.
Answers
GPT-4o mini
To solve the questions, let’s break down each part.
### Part A
To determine how many laps Dylan swims in 10 minutes, we need to relate time and distance.
1. **Distance per lap:** 1 lap = 25 yards
2. **Swimming rate:** Dylan swims 100 yards in 1.85 minutes.
To find the number of laps he swims in 10 minutes, we should set up a proportion involving time (in minutes) and distance (in yards).
**Step 1: Find the total distance Dylan swims in 10 minutes.**
- In 1.85 minutes, he swims 100 yards.
- In 10 minutes, we can set up the proportion as:
\[
\frac{1.85}{100} = \frac{10}{x}
\]
where \( x \) is the distance he swims in 10 minutes.
So the correct answer for Part A is:
**D.** \(\frac{1.85}{100} = \frac{10}{x}\)
### Part B
Next, to find out how many complete laps Dylan swims in 170 strokes, we first determine the number of strokes he takes for each yard and then find out the total number of yards he swims in 170 strokes.
1. **Strokes per minute:** 40 strokes
2. **Swimming rate:** Dylan swims 100 yards in 1.85 minutes, which is equivalent to calculating yards per stroke.
**Step 1: Find how many yards Dylan swims per stroke.**
- In 10 minutes, he swims \( \frac{10}{1.85} \times 100 \) yards.
- To find out the total number, we can also use the strokes. If he swims 100 yards in 1.85 minutes, the total number of strokes he takes in that time can be determined:
- In 1 minute, he makes 40 strokes. Therefore, in 1.85 minutes, he swims:
\[
40 \text{ strokes/min} \times 1.85 \text{ min} = 74 \text{ strokes}
\]
**Step 2: Find how many yards he swims per stroke:**
- Since he swims 100 yards in 74 strokes:
\[
\text{Yards per stroke} = \frac{100 \text{ yards}}{74 \text{ strokes}} \approx 1.3514 \text{ yards/stroke}
\]
**Step 3: Calculate total yards from 170 strokes:**
- Total yards in 170 strokes:
\[
\text{Total yards} = 170 \text{ strokes} \times 1.3514 \text{ yards/stroke} \approx 229.24 \text{ yards}
\]
**Step 4: Calculate the number of complete laps:**
- Since each lap is 25 yards:
\[
\text{Number of laps} = \frac{229.24 \text{ yards}}{25 \text{ yards/lap}} \approx 9.17 \text{ laps}
\]
So, the number of complete laps he swims is:
**Answer for Part B:** 9 complete laps.
### Part A
To determine how many laps Dylan swims in 10 minutes, we need to relate time and distance.
1. **Distance per lap:** 1 lap = 25 yards
2. **Swimming rate:** Dylan swims 100 yards in 1.85 minutes.
To find the number of laps he swims in 10 minutes, we should set up a proportion involving time (in minutes) and distance (in yards).
**Step 1: Find the total distance Dylan swims in 10 minutes.**
- In 1.85 minutes, he swims 100 yards.
- In 10 minutes, we can set up the proportion as:
\[
\frac{1.85}{100} = \frac{10}{x}
\]
where \( x \) is the distance he swims in 10 minutes.
So the correct answer for Part A is:
**D.** \(\frac{1.85}{100} = \frac{10}{x}\)
### Part B
Next, to find out how many complete laps Dylan swims in 170 strokes, we first determine the number of strokes he takes for each yard and then find out the total number of yards he swims in 170 strokes.
1. **Strokes per minute:** 40 strokes
2. **Swimming rate:** Dylan swims 100 yards in 1.85 minutes, which is equivalent to calculating yards per stroke.
**Step 1: Find how many yards Dylan swims per stroke.**
- In 10 minutes, he swims \( \frac{10}{1.85} \times 100 \) yards.
- To find out the total number, we can also use the strokes. If he swims 100 yards in 1.85 minutes, the total number of strokes he takes in that time can be determined:
- In 1 minute, he makes 40 strokes. Therefore, in 1.85 minutes, he swims:
\[
40 \text{ strokes/min} \times 1.85 \text{ min} = 74 \text{ strokes}
\]
**Step 2: Find how many yards he swims per stroke:**
- Since he swims 100 yards in 74 strokes:
\[
\text{Yards per stroke} = \frac{100 \text{ yards}}{74 \text{ strokes}} \approx 1.3514 \text{ yards/stroke}
\]
**Step 3: Calculate total yards from 170 strokes:**
- Total yards in 170 strokes:
\[
\text{Total yards} = 170 \text{ strokes} \times 1.3514 \text{ yards/stroke} \approx 229.24 \text{ yards}
\]
**Step 4: Calculate the number of complete laps:**
- Since each lap is 25 yards:
\[
\text{Number of laps} = \frac{229.24 \text{ yards}}{25 \text{ yards/lap}} \approx 9.17 \text{ laps}
\]
So, the number of complete laps he swims is:
**Answer for Part B:** 9 complete laps.