A new event in the Buck-Up Rodeo circuit is the Quarter Horse Mile, which is four laps around a racetrack. Colten entered his quarter horse, Jasper, in this race in three consecutive rodeos.

Question

Jasper completed his first race in exactly 4 1/2
 
 minutes, with an average lap time of 1.125
 minutes per lap.
In Jasper's second race, he changed his average lap time from the first race by -0.075
 minutes.
In Jasper's third race, he changed his total race time from the first race by -1.00
 minute.
Use the drop-down menus to correctly complete the statements.

In Jasper's second race, his total time from the first race changed by  
 minutes; his total race time was 
 minutes.
In Jasper's third race, his average lap time from his first race changed by  
 minutes; his average lap time was 
 minutes.

GPT-4o mini · Answer

Let's calculate each of the needed components step by step.

First Race:

Jasper's first race time is given as 4 1/2 minutes, which is: \[ 4.5 \text{ minutes} \]

His average lap time was: \[ 1.125 \text{ minutes per lap} \]

Second Race:

In Jasper's second race, his average lap time changed by -0.075 minutes from his first race.

First race average lap time: 1.125 minutes
Change: -0.075 minutes

Calculating the average lap time for the second race: \[ 1.125 - 0.075 = 1.050 \text{ minutes per lap} \]

For the total race time in the second race, since it is 4 laps: \[ 1.050 \text{ minutes per lap} \times 4 \text{ laps} = 4.200 \text{ minutes} \]

Now, calculating the change in total time from the first to the second race: Total time from the first race - Total time from the second race: \[ 4.5 - 4.200 = 0.300 \text{ minutes} \]

Third Race:

In Jasper's third race, his total race time changed by -1.00 minute from his first race. Calculating the total time for the third race: \[ 4.5 - 1.00 = 3.5 \text{ minutes} \]

To find the average lap time for the third race over 4 laps: \[ 3.5 \text{ minutes} \div 4 \text{ laps} = 0.875 \text{ minutes per lap} \]

Now, calculating the change in average lap time from the first race:

First race average lap time: 1.125 minutes
Third race average lap time: 0.875 minutes
Change: \[ 1.125 - 0.875 = 0.250 \text{ minutes} \]

Final Statements:

In Jasper's second race, his total time from the first race changed by 0.300 minutes; his total race time was 4.200 minutes.
In Jasper's third race, his average lap time from his first race changed by 0.250 minutes; his average lap time was 0.875 minutes.