Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided into 360 degree where 0 degrees is north and a bearing is measured clockwise from north.
A.) Gabino and Mia are taking part in an orienteering course. They are instructed to walk 2.3 km on a bearing of 305 degrees to reach point A. There they are supposed to change their bearing to 64 degrees and walk 3.1 km to reach point B. Next they are supposed o return to their original position C. If they walk at an average pace of 4.5 km/h, how long should they expect the entire trip to take?
To solve this problem, we need to calculate the total distance of the trip and divide it by the average pace.
First, let's calculate the distance from point C to point A:
Using the formula: Distance = Speed × Time
Distance_A = 2.3 km
Next, let's calculate the distance from point A to point B:
Distance_B = 3.1 km
Now, let's calculate the distance from point B back to point C:
Distance_C = Distance_A
Total distance = Distance_A + Distance_B + Distance_C
Now that we have the total distance, we can calculate the time it will take:
Time = Total distance / Average pace
Finally, let's substitute the given values into the formula:
Total distance = Distance_A + Distance_B + Distance_C = 2.3 km + 3.1 km + 2.3 km = 7.7 km
Average pace = 4.5 km/h
So, Time = Total distance / Average pace = 7.7 km / 4.5 km/h
To find the time, we divide the total distance by the average pace:
Time = 7.7 km / 4.5 km/h = 1.71 hours
This means that Gabino and Mia should expect the entire trip to take approximately 1.71 hours, or about 1 hour and 42 minutes.