12. An avalanche rescue team travels 8.55 km along a snow-covered trail. For the first section, the trail is flat. The team averages a speed of 2.7 km/h. Then, the terrain becomes mountainous and their average speed is only 1.2 km/h. The one-way trip takes the team 4.0 h. Determine the distance that the team travels on each type of terrain.
add up the times, knowing that time = distance/speed:
x/2.7 + (8.55-x)/1.2 = 4.0
x = 6.75
so,
6.75km flat
1.80km mtns
To determine the distance that the team travels on each type of terrain, we can use the formula:
Distance = Speed × Time
Let's calculate the distance traveled on the flat trail first.
1. Convert the average speed on the flat trail from km/h to km/min.
Speed on flat trail = 2.7 km/h = 2.7 km/60 min ≈ 0.045 km/min
2. Calculate the time spent on the flat trail.
Time on flat trail = 4.0 h - time spent on the mountainous terrain
= 4.0 h - time spent on the mountainous terrain = 4.0 h - (Distance on mountainous terrain ÷ Speed on mountainous terrain)
Now, let's calculate the distance traveled on the mountainous terrain.
1. Convert the average speed on the mountainous terrain from km/h to km/min.
Speed on mountainous terrain = 1.2 km/h = 1.2 km/60 min = 0.02 km/min
2. Calculate the time spent on the mountainous terrain.
Time spent on the mountainous terrain = 4.0 h - Time on flat terrain
3. Calculate the distance on the mountainous terrain.
Distance on mountainous terrain = Speed on mountainous terrain × Time on mountainous terrain
Now we have all the information needed to solve the problem. Let's plug the values into the formulas to find the distances.
Distance on flat trail = (Speed on flat trail) × (Time on flat trail)
Distance on mountainous terrain = (Speed on mountainous terrain) × (Time on mountainous terrain)
Once you've calculated both of these distances, you will have the answer to the question.