Julio went to Germany to watch an international soccer tournament. He first watched Argentina play Germany in Berlin, Germany. The next day Julio went to Frankfurt, Germany to watch Brazil play France.
To get from Berlin to Frankfurt for this second game, Julio took a bus from Berlin to Erfurt (\(303\) km); then he rented a car and drove from Erfurt to Frankfurt (\(254\) km). Julio drove on German highways, called autobahns, which have no general speed limit for passenger vehicles; however, buses have an enforced speed limit of \(80\) km/hr.
The distances are reported in whole kilometers, so it is likely that they are only accurate to the nearest kilometer, if that. A kilometer at 80 km/hr is 45 seconds, so it is unlikely that reporting the answer to an accuracy greater than the nearest minute will be meaningful. And, taking into account the possibility that the bus and car might drive at slower speeds getting to and from the autobahn, possibly compensating by exceeding the speed limit slightly on the autobahn, it seems reasonable to report times in a much broader range. Thus, rounding intermediate calculations to the hundredths place is more than sufficient.
One way to solve this is to note that Julio traveled a total of \(303+254 = 557\) miles over \(5.74\) hours, his average speed was $$\frac{557 \text{ km}}{5.74 \text{ hr}} = 97 \frac{\text{ km}}{\text{ hr}} \approx 100 \frac{\text{ km}}{\text{ hr}}.$$
Alternatively, since Julio has spent \(66\%\) of the time traveling at 80 km/hr and \(34\%\) of the time traveling at \(130\) km/hr, his average speed over the whole trip is given by $$ 0.66\times 80 + 0.34\times 130=97\frac{\text{ km}}{\text{ hr},} $$ which we again report as approximately 100 km/hr.
Commentary
This task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip.
At a higher level, the task addresses N-Q.3, since realistically neither the car nor the bus is going to travel at exactly the same speed from beginning to end of each segment; there is time traveling through traffic in cities, and even on the autobahn the speed is not constant. Thus students must make judgements about the level of accuracy with which to report the result.