Julio is at a car race. Starting from 0.5 miles away, the car drives toward him and then passes him. The car travels at a constant rate of 110 miles per hour. The distance of the car from Julio is given by d = |0.5 – 110t|. At what times is the car 0.05 miles from Julio? Calculate your answer in seconds.

Question

(1 point)
Responses

14.7s and 18.0s

100s and 110s

147s and 180s

1.5s and 1.8s

Answer 1

To find the times at which the car is 0.05 miles from Julio, we can set up the equation:

0.05 = |0.5 - 110t|

Since the distance cannot be negative, we can ignore the absolute value sign and solve for t:

0.05 = 0.5 - 110t

Subtract 0.5 from both sides:

-0.45 = -110t

Divide both sides by -110:

t = 0.45 / 110 ≈ 0.004091

Converting this to seconds, we multiply by 60 (to convert minutes to seconds) and 60 again (to convert hours to seconds):

t ≈ 0.004091 * 60 * 60 ≈ 14.75

Therefore, the car is 0.05 miles from Julio at approximately 14.75 seconds.