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 . At what times is the car 0.1 miles from the checkpoint? Calculate your answer in seconds

Question

across · Answer

The question may be incomplete, but I believe the distance of the car from the checkpoint should be modeled by an equation looking something like this:$$y=-53x+1.5$$Is this correct?

across · Answer

Let's keep in mind that the units of the above function are in miles per hour.

Now, we're asked to find at what time is the car 0.1 miles from the checkpoint. Well, all we have to do is modify our equation above a little and solve for $x$:$$0.1=-53x+1.5$$$$-1.4=-53x$$$$-1.4=-53x$$$$x=\frac{14}{530}$$But since the units of $x$ are in hours, we have to multiply that by $3600$:$$x=\frac{14}{530}\cdot3600\approx95$$This means that in about 95 seconds, the car will be 0.1 miles from the checkpoint.