supertanker during a crash stop.
time, t (min) | speed, s (km/h)
--- | ---
0 | 30
3 | 24
6 | 18
9 | 12
12 | 6
15 | 0
1. a) what do you think the speed will be at 4 min? 5 min?
b) describe the pattern you see in the data. what do you notice about how the values change from one set of coordinate pairs to the next?
2. a) on a graph, plot the coordinate pairs in the table.
b) which variable did you plot on the horizontal axis? why did you select that variable?
c) which variable did you plot on the vertical axis? why did you select that variable?
d) does the graph match your pattern description? explain.
3. write an equation to model the data on the graph.
4. a) what value did you choose for the numerical coefficient and the constant?
b) how did you determine each value?
5. a smaller tanker can stop in less time. the equation ( s = -3t + 30 ), where speed, ( s ), in km/h, and time, ( t ), in min, models the stopping of the smaller tanker.
a) what would be the speed of the tanker at 7 min? how did you determine your answer?
b) how much time would it take for the tanker to slow down to 8 km/h? compare your solution with that of a classmate. explain how you arrived at your answer.
in this chapter, you will explore mathematical relationships between variables, such as time and distance for different types of boats. at the end of the chapter, you will research and plan an adventure trip on water, showing mathematical relationships between variables.
literacy link
a metric tonne (t) is a measurement of mass that equals 1000 kg.
web link
for more information about supertankers and other oil tankers, go to www.mathlinks.ca and follow the links.

Question

supertanker during a crash stop.
time, t (min) | speed, s (km/h)
--- | ---
0 | 30
3 | 24
6 | 18
9 | 12
12 | 6
15 | 0
1. a) what do you think the speed will be at 4 min? 5 min?
   b) describe the pattern you see in the data. what do you notice about how the values change from one set of coordinate pairs to the next?
2. a) on a graph, plot the coordinate pairs in the table.
   b) which variable did you plot on the horizontal axis? why did you select that variable?
   c) which variable did you plot on the vertical axis? why did you select that variable?
   d) does the graph match your pattern description? explain.
3. write an equation to model the data on the graph.
4. a) what value did you choose for the numerical coefficient and the constant?
   b) how did you determine each value?
5. a smaller tanker can stop in less time. the equation ( s = -3t + 30 ), where speed, ( s ), in km/h, and time, ( t ), in min, models the stopping of the smaller tanker.
   a) what would be the speed of the tanker at 7 min? how did you determine your answer?
   b) how much time would it take for the tanker to slow down to 8 km/h? compare your solution with that of a classmate. explain how you arrived at your answer.
in this chapter, you will explore mathematical relationships between variables, such as time and distance for different types of boats. at the end of the chapter, you will research and plan an adventure trip on water, showing mathematical relationships between variables.
literacy link
a metric tonne (t) is a measurement of mass that equals 1000 kg.
web link
for more information about supertankers and other oil tankers, go to www.mathlinks.ca and follow the links.

Accepted Answer

### 1. a)
# Brief Explanations:
Look at the pattern in the table: every 3 minutes, speed decreases by 6 km/h. That means each minute, speed drops by $\frac{6}{3}=2$ km/h.
- At t=3, speed is 24 km/h. At t=4 (1 minute later), speed = $24 - 2 = 22$ km/h.
- At t=5 (2 minutes after t=3), speed = $24 - (2*2) = 20$ km/h.
The pattern is a linear decrease: speed drops by 2 km/h every minute as time increases.
# Answer:
Speed at 4 min: 22 km/h; Speed at 5 min: 20 km/h. The speed decreases by 2 km/h for every 1 minute increase in time, showing a steady linear downward trend.

---

### 2. a)
# Brief Explanations:
Plot the coordinate pairs (time, speed): (0,30), (3,24), (6,18), (9,12), (12,6), (15,0) on a graph, with each pair representing a point.
# Answer:
Plot the points (0, 30), (3, 24), (6, 18), (9, 12), (12, 6), (15, 0) on a Cartesian graph.

### 2. b)
# Brief Explanations:
Time is the independent variable (it is controlled/elapses on its own, not dependent on speed), so it is placed on the horizontal axis.
# Answer:
Horizontal axis: Time ($t$). Time is the independent variable that drives the change in speed.

### 2. c)
# Brief Explanations:
Speed depends on how much time has passed during the stop, so it is the dependent variable, placed on the vertical axis.
# Answer:
Vertical axis: Speed ($s$). Speed is the dependent variable that changes as time increases.

### 2. d)
# Brief Explanations:
The graph will be a straight line sloping downward from left to right, which matches the steady linear decrease in speed as time increases observed in the data.
# Answer:
Yes, the graph matches. It is a straight, downward-sloping line, which shows speed decreases steadily by 2 km/h per minute, consistent with the data pattern.

---

### 3.
# Explanation:
## Step1: Identify linear form
The relationship is linear, so use $s=mt+b$, where $m$ = slope, $b$ = y-intercept.
## Step2: Calculate slope ($m$)
Slope = $\frac{	ext{Change in } s}{	ext{Change in } t} = \frac{24-30}{3-0} = \frac{-6}{3} = -2$
## Step3: Find y-intercept ($b$)
When $t=0$, $s=30$, so $b=30$.
## Step4: Write the equation
Substitute $m=-2$ and $b=30$ into the linear form.
# Answer:
$s = -2t + 30$

---

### 4. a)
# Brief Explanations:
In the equation $s=-2t+30$, the numerical coefficient is $-2$ (multiplied by the independent variable $t$), and the constant is $30$ (the fixed starting value).
# Answer:
Numerical coefficient: $-2$; Constant: $30$

### 4. b)
# Brief Explanations:
- The coefficient $-2$ is calculated from the rate of change of speed over time: $\frac{	ext{Change in speed}}{	ext{Change in time}} = \frac{-6}{3} = -2$.
- The constant $30$ is the initial speed when $t=0$ (from the table, at 0 minutes, speed is 30 km/h).
# Answer:
- The coefficient $-2$ is the rate of speed decrease: speed drops 2 km/h per minute, calculated from the change in speed divided by change in time.
- The constant $30$ is the initial speed of the supertanker at $t=0$ minutes, taken directly from the table.

---

### 5. a)
# Explanation:
## Step1: Use given equation
The model is $s=-3t+30$. Substitute $t=7$.
## Step2: Calculate speed
$s = -3(7) + 30 = -21 + 30$
# Answer:
9 km/h. Substitute $t=7$ into $s=-3t+30$: $s=-21+30=9$ km/h.

### 5. b)
# Explanation:
## Step1: Set up the equation
Substitute $s=8$ into $s=-3t+30$.
## Step2: Solve for $t$
$8 = -3t + 30$
$3t = 30 - 8$
$t = \frac{22}{3} \approx 7.33$
# Answer:
$\frac{22}{3}$ minutes (or approximately 7.33 minutes). Substitute $s=8$ into $s=-3t+30$, rearrange to solve for $t$: $3t=30-8=22$, so $t=\frac{22}{3}$.

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