Question

The distance in miles of a motorist from her destination is given by the function d(t) = 468 – 65t, where d(t) is the distance and t is the time she has been traveling, in hours. How long has the motorist been traveling when she is 299 miles from her destination?

Answer 1

By solving the equation 468 - 65t = 299 for t, we find that the motorist has been traveling for about 2.6 hours when 299 miles away from her destination.

Step-by-step explanation:

The question is asking for the time at which the motorist is 299 miles away from her destination. This corresponds to the point when d(t) = 299 in the function d(t) = 468 - 65t.

To find this, you would need to solve the equation 468 - 65t = 299 for t. Subtract 299 from both sides of the equation to get -65t = -169. Divide both sides by -65 to solve for t. Hence, t is equal to 169/65, or approximately 2.6 hours.

Therefore, the motorist has been traveling for about 2.6 hours when 299 miles from her destination.

Learn more about Solving Linear Equations