Exercise 30 Page 827

We want to determine how many minutes a trip made on a personal watercraft took.

We are told that a person travels 28 miles per hour from point A to B and from B to C, and 35 miles per hour from point C to A. Before finding the time of a whole trip, we need to determine the distance between A and C. We will do this using the Law of Cosines.

For our triangle the known side lengths are 0.15 and 0.25, and the included angle measure is 130^(∘). We will call the missing side length b. Let's substitute these values into the Law of Cosines and find the value of b.

Note that since a negative side length does not make sense, we only need to consider the positive solutions. Let's add the obtained information to the diagram.

Now we can calculate how long the trip took. Recall that in the Distance Formula d stands for distance, t stands for time, and r stands for the rate of change — in this case, the speed. If we transform the formula we will get the rule for time. d=rt ⇔ t=d/r Let's start by calculating the time of the first part of the trip, from Point A to B and then to C. The distance of this part of the trip would be the sum of distances between points A and B, and B and C. The speed was 28 miles per hour.

Recall that we wanted our solution in minutes. We will use the fact that 1 hour is 60 minutes to change the unit to minutes.

Now we will find the time of the second part of the trip. The distance between points A and C is 0.36 miles and the speed was 35 miles per hour.

Once again we need to change hours into minutes.

The total time of the trip is the sum of the two times we obtained for the parts of the trip. 0.9min+0.6min=1.5min The total time of the trip was approximately 1.5 minutes.