Question

Starting from 1.5 miles away, a car drives towards a speed checkpoint and then passes it. The car travels at a constant rate of 53 miles per hour. The distance of the car from the checkpoint is given by d=l1.5-53tl . At what times is the car 0.1 miles from the checkpoint? Calculate your answer in seconds.
95.1s and 108.7s
10.2s and 101.9s
108.7s and 10.2s
95.1s and 10.2s

Answer 1

\[d=|1.5-53t|\]where d is in miles and t is in hours.
first divide both sides by 53 to get:\[\frac{d}{53}=|\frac{1.5}{53}-t|\]this can be split into two portions:

(1) for t <= 1.5/53 hours we can write:\[\frac{d}{53}=\frac{1.5}{53}-t\]\[t=\frac{1.5-d}{53}\]

(2) for t > 1.5/53 hours we can write:\[\frac{d}{53}=-(\frac{1.5}{53}-t)=t-\frac{1.5}{53}\]\[t=\frac{1.5+d}{53}\]

now just stick the value d=0.1 into (1) and (2) above to get your answer (remember to multiply the answers you get by 3600 to convert hours to seconds).

Answer 2

thank you so much

Answer 3

yw