Point A and B are 17km apart if you follow the path. A troop of boy scouts leaves point A at 11:00 AM. They are all carrying packs and travel 4km/h until they reach point C at 13:25. From point C , if they want to reach point B by 14:30, how fast will they have to go?
To find the time it took for the boy scouts to travel from point A to point C, we subtract the starting time from the arrival time:
13:25 - 11:00 = 2 hours and 25 minutes
We convert the 25 minutes to hours by dividing by 60:
25 minutes ÷ 60 = 0.4167 hours
So the total time it took to travel from point A to point C is 2 + 0.4167 = 2.4167 hours.
The distance between point A and C is 17 km.
Their speed is 4 km/h, so we can use the formula time = distance / speed to find their travel time from point A to C:
2.4167 hours = 17 km / speed
To find their speed, we rearrange the formula:
speed = distance / time
speed = 17 km / 2.4167 hours
speed = 7.04 km/h
To find out how fast they will have to go from point C to point B, we need to find the remaining distance:
Distance from point C to point B = Total distance - Distance from point A to point C
Distance from point C to point B = 17 km - 17 km
Distance from point C to point B = 0 km
Since the remaining distance is 0 km, they don't have to go anywhere.
To determine the speed required to travel from point C to point B in the given time frame, we need to calculate the remaining distance and the available time.
Let's start by finding the time taken to travel from point A to point C:
Total time taken = 13:25 - 11:00 = 2 hours and 25 minutes
= 2.42 hours (since 25 minutes is 0.42 hours)
Since the troop travels at a speed of 4 km/h, we can calculate the distance covered from point A to point C:
Distance traveled from A to C = Speed * Time
= 4 km/h * 2.42 hours
= 9.68 km
Now, let's determine the remaining distance from point C to point B:
Remaining distance = Total distance - Distance from A to C
= 17 km - 9.68 km
= 7.32 km
To find the time available to travel from point C to point B:
Time available = 14:30 - 13:25
= 1 hour and 5 minutes
= 1.08 hours (since 5 minutes is 0.08 hours)
Finally, we can calculate the speed needed to travel the remaining distance in the available time:
Required speed = Remaining distance / Time available
= 7.32 km / 1.08 hours
≈ 6.78 km/h
Therefore, the troop of boy scouts will have to travel at a speed of approximately 6.78 km/h to reach point B by 14:30.
To find out how fast the boy scouts will have to go from point C to point B, we first need to determine the remaining distance between C and B.
Given that point A and point B are 17km apart, and the scouts traveled from point A to point C, we can calculate the distance between C and B by subtracting the distance traveled from the total distance:
Distance between C and B = Total distance (A to B) - Distance traveled (A to C)
Distance between C and B = 17km - 4km
Distance between C and B = 13km
Since the scouts have to reach point B by 14:30, we need to calculate the time available for them to cover the remaining distance.
Time available = Desired time (14:30) - Time spent traveling from A to C (13:25)
To calculate the time spent traveling from A to C, we need to convert the time spent to a decimal representation:
Time spent = Hours + (Minutes / 60) = 13 + (25 / 60) = 13.42 hours
Desired time = 14 + (30 / 60) = 14.5 hours
Time available = 14.5 - 13.42 = 1.08 hours
Now, we can calculate the speed required to cover the remaining distance within the given time.
Speed = Distance / Time
Speed = 13km / 1.08 hours
Speed ≈ 12.04 km/h
Therefore, the boy scouts will have to travel at a speed of approximately 12.04 km/h from point C to point B in order to reach point B by 14:30.