Points A and B on a map are 15 km apart if you follow the path. A troop of boy scouts leaves point A at 11:00 a.m. They are all carrying packs and travel 4 km/h until they reach point C at 12:25pm. From point C, if they want to reach point B by 14:00pm, how fast will they have to go?
From 11:00 a.m. to 12:25 p.m. is 1 hour and 25 minutes, or 1.42 hours.
Traveling at 4 km/h, they would cover a distance of 4 km/h * 1.42 h = 5.68 km.
So, they would be at point C, which is 15 km - 5.68 km = 9.32 km away from point B.
They have 1 hour and 35 minutes, or 1.58 hours, to cover a distance of 9.32 km to reach point B.
Thus, they will have to go at a speed of 9.32 km / 1.58 h ≈ <<9.32/1.58=5.90>>5.90 km/h to reach point B by 14:00pm. Answer: \boxed{5.90}.
To solve this problem, we can first determine the time taken to travel from point A to point C. We can then calculate the remaining time available to reach point B from point C. With this information, we can find the required speed to cover the remaining distance.
Given:
Distance from A to B: 15 km
Time taken from A to C: 12:25 pm - 11:00 am = 1 hour and 25 minutes = 1.42 hours (approximately)
Time available from C to B: 14:00 pm - 12:25 pm = 1 hour and 35 minutes = 1.58 hours (approximately)
To find the speed required from C to B, we can use the formula:
Speed = Distance / Time
To find the remaining distance, we subtract the distance covered from the total distance:
Remaining distance = Total distance - Distance from A to C
= 15 km - 4 km
= 11 km
Now, we can calculate the required speed:
Required speed from C to B = Remaining distance / Time available from C to B
= 11 km / 1.58 hours
≈ 6.96 km/h
Therefore, the boy scouts will have to travel at a speed of approximately 6.96 km/h to reach point B by 14:00 pm from point C.
To determine the speed required to reach point B from point C on time, we need to calculate the remaining distance and the available time.
Given:
Distance between A and B = 15 km
Time taken from A to C = 1 hour and 25 minutes = 1.41 hours
Required time from C to B = 2 hours
Total available time from C to B = 2 - 1.41 = 0.59 hours
Remaining distance from C to B = 15 - 4 = 11 km
To find the required speed, we divide the distance by the time:
Required speed = Remaining distance / Available time
Required speed = 11 km / 0.59 hours
Required speed ≈ 18.64 km/h
Therefore, the boy scouts will have to travel at a speed of approximately 18.64 km/h to reach point B by 14:00pm.