Final answer:
The time it takes for Jon Kimm to complete the race is approximately 203.697 seconds.
Step-by-step explanation:
To calculate the time it takes for Jon Kimm to complete the race, we need to find the total distance he travels and divide it by his average speed.
The first 3 laps are completed at 195 mph, so the distance covered in those laps is 3d (since d represents the length of one lap).
The remaining laps are completed at 205 mph, so the distance covered in those laps is 12d (since there are 15 laps in total and 3 have already been completed).
The total distance covered is 3d + 12d = 15d.
To find the time, we divide the total distance by the average speed.
The average speed is the total distance divided by the total time. Since we don't have the total time, we'll keep it as a variable t.
Therefore, the equation becomes:
15d/t = (3d/195) + (12d/205)
To solve for t, we can cross multiply:
15d = (3d/195) * t + (12d/205) * t
15dt = 3dt/195 + 12dt/205
Applying the same denominator, we get:
15dt = (205 * 3dt + 195 * 12dt) / (195 * 205)
Simplifying further:
15dt = (615dt + 2340dt) / 39975
Combining like terms:
15dt = 2955dt / 39975
Dividing both sides by dt:
15 = 2955 / 39975
Multiplying both sides by dt:
dt = (15 * 39975) / 2955
Finally, simplifying the expression gives us:
dt = 203.697 seconds