The 250 meters between S's house and the tennis court corresponds to 5 cm on a town map. What is the actual distance between S's school and the library if they are 8.4 cm apart on the same the map?
Since 250 meters corresponds to 5 cm on the map, then 8.4 cm on the map corresponds to 250/5 * 8.4 = 420 meters. Answer: \boxed{420}.
A biker cycles 9 miles in 2/3 of an hour. What is his average speed in milews per hour?
To find the average speed, we divide the total distance traveled by the total time taken. In this case, the biker traveled 9 miles in 2/3 of an hour, which is $\frac{9}{\frac{2}{3}} = 9 \cdot \frac{3}{2} = \boxed{13.5}$ miles per hour.
To find the actual distance between S's school and the library, we need to use the scale of the map, which tells us the relationship between the distances on the map and the actual distances in reality. In this case, we know that 250 meters corresponds to 5 cm on the map.
First, let's calculate the scale of the map. We can do this by finding the ratio of the distances on the map to the actual distances.
Ratio = Actual Distance / Map Distance
Using the given information, we have:
Ratio = 250 meters / 5 cm
To make sure the units are consistent, we need to convert meters to centimeters:
Ratio = (250 meters * 100 cm/meter) / 5 cm
Ratio = 50000 cm / 5 cm
Ratio = 10000
Now that we have the scale of the map, we can use it to find the actual distance between S's school and the library. According to the map, they are 8.4 cm apart.
Actual Distance = Map Distance * Ratio
Actual Distance = 8.4 cm * 10000
Actual Distance = 84000 cm
Therefore, the actual distance between S's school and the library is 84000 cm.