To find out how long Gabino and Mia should expect the entire trip to take, we need to calculate the time it takes for each leg of the journey and then sum up the times.
First, let's calculate the time it takes for Gabino and Mia to walk 2.3 km on a bearing of 305 degrees to reach point A. To do this, we use the formula:
Time = Distance / Speed
Distance = 2.3 km
Speed = 4.5 km/h
Plugging in the values, we get:
Time(A) = 2.3 km / 4.5 km/h
Time(A) ā 0.5111 hours
Next, let's calculate the time it takes for them to change their bearing to 64 degrees and walk 3.1 km to reach point B. Again, using the formula:
Time = Distance / Speed
Distance = 3.1 km
Speed = 4.5 km/h
Plugging in the values, we get:
Time(B) = 3.1 km / 4.5 km/h
Time(B) ā 0.6889 hours
Now, they need to return to their original position C. The distance from point B to point C is the same as the distance from point A to point B, which is 3.1 km.
Time(C) = Distance / Speed
Distance = 3.1 km
Speed = 4.5 km/h
Plugging in the values, we get:
Time(C) = 3.1 km / 4.5 km/h
Time(C) ā 0.6889 hours
Now, let's sum up the times for each leg of the journey:
Total Time = Time(A) + Time(B) + Time(C)
Total Time ā 0.5111 hours + 0.6889 hours + 0.6889 hours
Total Time ā 1.8889 hours
Therefore, Gabino and Mia should expect the entire trip to take approximately 1.8889 hours.