Question

1. Brandon went to a Formula One car race and used his stopwatch to time how fast his favorite driver, Fernando Alonso, went around the 4.7-kilometer track. Brandon started the timer at the beginning of the second lap, when the cars were already going fast. When he stopped the timer at the beginning of the third lap, one minute and three seconds had passed.

b. If you graphed the distance Fernando had traveled at the beginning of the lap and at the end of the lap, what would the coordinates of these points be? What would the

- and

-axes on this graph represent?

c. Find the equation of the line between these two points. What does this line represent?

d. If Fernando continues to average this speed, about how long do you think it would take him to finish the entire race? The race is 500 km.

Answer 1

Explanation:

b. To determine the coordinates of the points on the graph, we need to consider the information given.

At the beginning of the second lap, one minute and three seconds had passed. Since each lap is 4.7 kilometers long, we can calculate the distance traveled at the beginning of the lap using the formula:

Distance = (Number of laps - 1) × Length of each lap

For the beginning of the second lap:

Distance = (2 - 1) × 4.7 km = 4.7 km

At the beginning of the third lap, one minute and three seconds had passed. Therefore, the distance traveled at the beginning of the third lap is:

Distance = (3 - 1) × 4.7 km = 9.4 km

The coordinates of the points on the graph would be:

Point A: (4.7 km, 4.7 km)

Point B: (9.4 km, 9.4 km)

On the graph, the x-axis would represent the distance traveled at the beginning of the lap, and the y-axis would represent the distance traveled at the end of the lap.

c. To find the equation of the line between the two points, we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

Using the coordinates of the two points (4.7 km, 4.7 km) and (9.4 km, 9.4 km), we can calculate the slope:

m = (y2 - y1) / (x2 - x1)

= (9.4 km - 4.7 km) / (9.4 km - 4.7 km)

= 4.7 km / 4.7 km

= 1

The slope of the line is 1.

Since the line passes through the origin (0, 0), the y-intercept (b) is 0.

Therefore, the equation of the line is:

y = 1x + 0

y = x

This line represents a one-to-one relationship between the distance traveled at the beginning of the lap and the distance traveled at the end of the lap.

d. To estimate how long it would take Fernando to finish the entire race if he continues to average the same speed, we need to find the time it takes for one lap.

In the given scenario, Brandon timed Fernando's lap for one minute and three seconds. Since there are 3 laps in total, we can divide the total time by the number of laps to find the average time per lap:

Average time per lap = Total time / Number of laps

= 1 minute and 3 seconds / 3

= 21 seconds

Since each lap is 4.7 kilometers long, we can calculate the speed:

Speed = Distance / Time

= 4.7 km / (1 minute + 21 seconds)

To estimate the time it would take Fernando to finish the entire race, we divide the total race distance by the speed:

Total race time = Total race distance / Speed

= 500 km / (4.7 km / (1 minute + 21 seconds))

To calculate the time, we need to convert 1 minute and 21 seconds to a decimal form:

1 minute + 21 seconds = 1 minute + (21 seconds / 60 seconds)

= 1 minute + 0.35 minutes

= 1.35 minutes

Substituting the values:

Total race time = 500 km / (4.7 km / 1.35 minutes)

= 500 km × (

1.35 minutes / 4.7 km)

= 500 km × 0.28723...

≈ 143.615 minutes

Therefore, it would take approximately 143.615 minutes for Fernando to finish the entire race if he continues to average the same speed.