Question

One of the famous Grand Prix races takes place in Monaco, a small country south of France and West of Italy. Each Spring, racers from around the world come to this prestigious event. Currently, the race has 78 laps through the town of Monte Carlo (you may have seen this famous event in Iron Man 2). Each lap of the race has a distance of 3.34 km

What is the total length of the Monaco Grand Prix race?
a) 260.52 km
b) 261.52 km
c) 262.52 km
d) 263.52 km

Write a rational function for the race, where the independent variable is the average speed (in Km/hour) and the dependent variable is the time (in hours) to complete the race. What kind of variation is this?
a) Direct variation
b) Inverse variation
c) Joint variation
d) Combined variation
To the nearest km/hour, how much faster was the average winning speed in 2009 than in 2018?
a) 24 km/hour
b) 25 km/hour
c) 26 km/hour
d) 27 km/hour

In the 2018 qualifiers, Daniel Ricciardo set a new lap record of 1 minute, 11.841 seconds. What was his average speed for that lap?
a) 178.764 km/hour
b) 179.764 km/hour
c) 180.764 km/hour
d) 181.764 km/hour

Answer 1

The total length of the Monaco Grand Prix race is 260.52 km. The rational function for the race represents inverse variation. The average winning speed in 2009 was 27 km/h faster than in 2018. Daniel Ricciardo's average speed for his lap was 178.764 km/h.

Step-by-step explanation:

The total length of the Monaco Grand Prix race can be calculated by multiplying the distance of one lap (3.34 km) by the number of laps (78). So the total length is: 3.34 km/lap × 78 laps = 260.52 km.

A rational function for the race can be written as Time = Distance / Speed. Since the independent variable is the average speed (in km/hour) and the dependent variable is the time (in hours) to complete the race, this is an example of inverse variation.

To find how much faster the average winning speed in 2009 was than in 2018, subtract the average speeds of the two years: 2009 average speed - 2018 average speed = 280 km/h - 253 km/h = 27 km/h.

To calculate the average speed for Daniel Ricciardo's lap with a time of 1 minute, 11.841 seconds, convert the time to hours and divide the distance by the time: Average speed = Distance / Time = 3.34 km / (1.1974 hours) = 178.764 km/h.