the men are camping 45 miles due west and then go 60 miles directly north. if they can cover 18 miles a day how long will it take them to reach the railroad?
Assuming
(1) they can go straight cross-country
(2) they camped due west of the railroad
then the must travel
√(45^2+60^2) = 15√(3^2+4^2) = 75 miles
so, it will take them 75/18 = 25/6 days
To find out how long it will take the men to reach the railroad, we first need to calculate the total distance they will be traveling.
Given that they are camping 45 miles due west and then going 60 miles directly north, we can use the Pythagorean theorem to find the total distance they will be traveling:
Total distance = √((west distance)^2 + (north distance)^2)
Since the west distance is 45 miles and the north distance is 60 miles:
Total distance = √(45^2 + 60^2) = √(2025 + 3600) = √5625 = 75 miles
Now we can determine how long it will take to cover this distance, considering they can cover 18 miles a day.
Time = Total distance / Speed
Time = 75 miles / 18 miles/day ≈ 4.17 days
Therefore, it will take approximately 4.17 days for the men to reach the railroad. Keep in mind that this is an estimate, and factors such as terrain, weather conditions, and individual capabilities may affect the actual time it takes.