Question: 5. A cheetah has several speed runs from a point to the finish line.
The runs are shown in the following graph. How many meters would it travel in 1 second?
A. What is the unit rate in km per hour?
B. What is the unit rate in miles per hour, to the nearest tenth?
C. Write an equation for the number of miles y that the cheetah travels in x hours, and use it to solve the problem.
5. Sheryl reads at a rate of 75 pages per hour. The number of pages she reads each time is shown in the table.
Time (h) 1 5 7 10
Pages 75 375 525 600
A. What has a greater rate of reading?
B. At these rates, what is the difference in the number of pages if you read in 4 hours?
C. How long will it take each student to read a book with 760 pages?
Show your work
1. **Problem Statement:**
We have two problems:
- First, a cheetah's speed runs are shown on a graph, and we need to find how many meters it travels in 1 second, its unit rate in km/h, its unit rate in mph, and an equation for miles traveled.
- Second, Sheryl reads at 75 pages per hour, and we compare reading rates, differences in pages read in 4 hours, and time to read 760 pages.
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### Part 1: Cheetah Speed
2. **Find meters traveled in 1 second:**
Assuming the graph shows the cheetah's speed in miles per hour (mph). Let's say the speed is $s$ mph.
- 1 mile = 1609.34 meters
- 1 hour = 3600 seconds
So, meters per second (m/s) = $$s \times \frac{1609.34}{3600}$$
If the graph shows the cheetah runs at about 60 mph (typical cheetah speed), then:
$$\text{meters per second} = 60 \times \frac{1609.34}{3600} = 60 \times 0.44704 = 26.8224$$ meters per second.
3. **Unit rate in km per hour:**
- 1 mile = 1.60934 km
So, $$\text{speed in km/h} = s \times 1.60934$$
For $s=60$ mph:
$$60 \times 1.60934 = 96.5604$$ km/h
4. **Unit rate in miles per hour (to nearest tenth):**
Given speed $s$ mph, round to nearest tenth.
For example, if $s=60.2$ mph, rounded is 60.2 mph.
5. **Equation for miles traveled $y$ in $x$ hours:**
The distance traveled is speed times time:
$$y = s \times x$$
If $s=60$ mph, then:
$$y = 60x$$
To find distance in miles for a given time $x$ hours, plug in $x$.
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### Part 2: Reading Rates
6. **Given data:**
| Time (h) | 1 | 5 | 7 | 10 |
|----------|---|---|---|----|
| Pages | 75|375|525|600 |
7. **Calculate rates for each time:**
Rate = pages / time
- At 1 hour: $$\frac{75}{1} = 75$$ pages/hour
- At 5 hours: $$\frac{375}{5} = 75$$ pages/hour
- At 7 hours: $$\frac{525}{7} = 75$$ pages/hour
- At 10 hours: $$\frac{600}{10} = 60$$ pages/hour
So, the rate is mostly 75 pages/hour except at 10 hours where it is 60 pages/hour.
8. **A. What has a greater rate of reading?**
- Sheryl reads at 75 pages/hour.
- The 10-hour rate is 60 pages/hour.
So, Sheryl has a greater reading rate.
9. **B. Difference in pages read in 4 hours:**
- Sheryl: $$75 \times 4 = 300$$ pages
- Other rate (60 pages/hour): $$60 \times 4 = 240$$ pages
Difference: $$300 - 240 = 60$$ pages
10. **C. Time to read 760 pages:**
- Sheryl: $$\frac{760}{75} = 10.1333...$$ hours, about 10.13 hours
- Other rate (60 pages/hour): $$\frac{760}{60} = 12.6667$$ hours, about 12.67 hours
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**Final answers:**
- Cheetah travels about 26.8 meters in 1 second (assuming 60 mph).
- Unit rate in km/h: about 96.6 km/h.
- Unit rate in mph: 60.0 mph (example).
- Equation: $$y = 60x$$ miles.
- Sheryl reads faster at 75 pages/hour.
- Difference in pages read in 4 hours: 60 pages.
- Time to read 760 pages: Sheryl 10.13 hours, other 12.67 hours.